Libraries¶
In [1]:
# import libraries
import numpy as np
import scipy as sp
import networkx as nx
import matplotlib.pyplot as plt
Parameters¶
In [2]:
# Create an empty graph
G = nx.Graph()
# Add nodes
nodes = range(1, 17)
G.add_nodes_from(nodes)
# Add edges based on the visual structure
edges = [
(1, 2), (1, 3), (1, 4), (2, 4), (2,5), (3, 4), (3, 6), (3, 7), (3, 8), (4, 5), (4, 8), (4, 9),
(5, 9), (6, 7), (7, 8), (7, 11), (7, 10), (7, 13), (8, 9), (8, 11), (8, 12), (9, 12),
(10, 13), (11, 12), (11, 13), (11, 14), (12, 14), (12, 15), (13, 14), (13, 16) ,(14, 15),
(14, 16), (15, 16)
]
G.add_edges_from(edges)
# Set parameters
alpha = 0.0050415
beta = 0.000013047
delta = 0.0079639
do = 0.0017783
numerator = 2 * delta**2 * beta + do * (alpha + beta)**2 + 2 * (alpha + beta) * delta * np.sqrt(2 * do * (alpha + beta))
denominator = 2 * alpha * delta**2
Ic = numerator / denominator
I = Ic + 0.1
# Critical eigenvalue, must be 1.19198455
lambda_c = (do * (alpha + beta)**2 + 2 * beta * delta**2 - 2 * I * alpha * delta**2) / (4 * do * delta * (alpha + beta))
# Compute the homogeneous steady states
rho_ss = alpha * delta / (alpha + beta)
O_ss = (alpha + beta) / delta
params = {
'alpha': alpha,
'beta': beta,
'delta': delta,
'do': do,
'I': I,
'rho_ss': rho_ss,
'O_ss': O_ss,
'lambda_c': lambda_c
}
In [3]:
params
Out[3]:
{'alpha': 0.0050415,
'beta': 1.3047e-05,
'delta': 0.0079639,
'do': 0.0017783,
'I': np.float64(0.7074034423516578),
'rho_ss': 0.007943343261028139,
'O_ss': 0.6346823792363039,
'lambda_c': np.float64(-1.415470896407335)}
Dispertion Relation¶
In [6]:
def dispertion_relation(params, plot=False):
"""
Function to get the dispersion relation of the graph
"""
# Parameters
alpha = params['alpha']
beta = params['beta']
delta = params['delta']
do = params['do']
I = params['I']
rho_ss = params['rho_ss']
O_ss = params['O_ss']
lambda_c = params['lambda_c']
# Define a suitable range of lambda values
lambda_vals = np.linspace(-8, 0, 500)
# b(λ)
def b(lambda_N):
return ((alpha + beta)/delta
+ (delta * beta)/(alpha + beta)
- lambda_N * (2 + do))
# c(λ)
def c(lambda_N):
return (
2 * do * (lambda_N**2)
+ lambda_N * (
(2 * I * alpha * delta) / (alpha + beta)
- (2 * delta * beta) / (alpha + beta)
- (do * (alpha + beta)) / delta
)
+ (alpha + beta)
)
# η(λ) = -b(λ)/2 + (1/2)*sqrt(b(λ)^2 - 4 c(λ))
def eta(lambda_N):
return -0.5 * b(lambda_N) + 0.5 * np.sqrt(b(lambda_N)**2 - 4 * c(lambda_N))
# Evaluate eta on the grid of lambda values
eta_vals = eta(lambda_vals)
# Extract only the real part
eta_vals_real = np.real(eta_vals)
# Determine the range for positive values
positive_range = np.where(eta_vals_real > 0)[0]
min_lambda = lambda_vals[positive_range[0]]
max_lambda = lambda_vals[positive_range[-1]]
if plot:
# Plot the real part of eta vs. lambda
plt.figure()
plt.plot(lambda_vals, eta_vals_real, label=r'Real[$\eta(\lambda)$]')
# Graph a horizontal line at 0
plt.axhline(0, color='black', linestyle='-')
plt.xlabel(r'$\lambda$')
plt.ylabel(r'Real[$\eta(\lambda)$]')
plt.title('Plot of Real($\eta(\lambda)$) vs. $\lambda$')
plt.legend()
plt.grid(True)
plt.show()
return {
'min_lambda': float(min_lambda),
'max_lambda': float(max_lambda),
}
In [7]:
dispertion_relation(params)
Out[7]:
{'min_lambda': -2.1643286573146296, 'max_lambda': -0.6573146292585177}
Dynamics¶
In [9]:
# Set of functions
def get_dynamics(graph, params, plot=False):
"""
Function to get the dynamics of the graph
"""
# Parameters
alpha = params['alpha']
beta = params['beta']
delta = params['delta']
do = params['do']
I = params['I']
rho_ss = params['rho_ss']
O_ss = params['O_ss']
lambda_c = params['lambda_c']
G = graph
n = G.number_of_nodes()
e = G.number_of_edges()
A = nx.adjacency_matrix(G).todense()
def system(t, y, A, alpha, beta, delta, do, I):
"""
y[k][0] is rho
y[k][1] is O
n repetitions for each municipality
2 variables, rho and O
"""
y = y.reshape(n, 2)
dydt = np.zeros_like(y)
def function_1(j):
return A[i][j] * (y[j][0] - y[i][0])
def function_2(j):
return A[i][j] * ((y[i][1]/y[j][1])**I * y[j][0] - (y[j][1]/y[i][1])**I * y[i][0])
def function_3(j):
return A[i][j] * (y[j][1] - y[i][1])
j = np.arange(16)
for i in range(n):
f_1_j = np.vectorize(function_1)(j)
f_2_j = np.vectorize(function_2)(j)
f_3_j = np.vectorize(function_3)(j)
dydt[i, 0] = -y[i, 0] * y[i, 1] + alpha + np.sum(f_1_j) + np.sum(f_2_j)
dydt[i, 1] = -delta * y[i, 1] + beta + y[i, 0] * y[i, 1] + do * np.sum(f_3_j)
return dydt.flatten()
# Initial conditions
np.random.seed(0)
y0 = np.random.uniform(0.01, 2, n * 2)
# Time span
t_span = (0, 1000)
t_eval = np.linspace(*t_span, 100)
# Solve the system of ODEs
print("Starting the integration...")
solution = sp.integrate.solve_ivp(system, t_span, y0, method='BDF', args=(A, alpha, beta, delta, do, I), t_eval=t_eval)
print("Integration finished.")
t = solution.t
y = solution.y.reshape(n, 2, -1)
# Extract the stationary state from the dynamics (the last values)
nodes = np.arange(1, n + 1)
last_values_rho = np.zeros(n)
last_values_O = np.zeros(n)
for i in range(n):
last_values_rho[i] = y[i, 0][-1]
last_values_O[i] = y[i, 1][-1]
print("Linear algebra computations...")
# Computing the spectrum of the Laplacian matrix
L = -1 * nx.laplacian_matrix(G).todense()
eigenvalues, eigenvectors = np.linalg.eig(L)
# get the index of the nearest eigenvalue to lambda_c
index_lambda_c = np.argmin(np.abs(eigenvalues - lambda_c))
# the index cannot be zero
min_lambda, max_lambda = dispertion_relation(params).values()
# check if the index is in the range
critical_eigenvalue = eigenvalues[index_lambda_c]
linear_analysis = True
if critical_eigenvalue < min_lambda or critical_eigenvalue > max_lambda:
linear_analysis = False
if linear_analysis:
critical_eigenvector = eigenvectors[:, index_lambda_c]
else:
critical_eigenvector = np.zeros(n)
print("The critical eigenvalue is not in the range of the dispersion relation.")
print("The linear analysis cannot be performed.")
print("The critical eigenvalue is: ", critical_eigenvalue)
if plot:
# Creating the stem plots
fig, axes = plt.subplots(3, 1, figsize=(10, 10))
axes[0].stem(nodes, last_values_rho, linefmt='gray', markerfmt='ko', basefmt=' ', bottom=rho_ss)
axes[0].axhline(rho_ss, color='red', linestyle='--')
# Labeling the axes
axes[0].set_xlabel('Nodes')
axes[0].set_ylabel('rho')
axes[1].stem(nodes, last_values_O, linefmt='gray', markerfmt='ko', basefmt=' ', bottom=O_ss)
axes[1].axhline(O_ss, color='red', linestyle='--')
# Labeling the axes
axes[1].set_xlabel('Nodes')
axes[1].set_ylabel('O')
axes[2].stem(nodes, critical_eigenvector, linefmt='gray', markerfmt='ko', basefmt=' ')
axes[2].axhline(0, color='red', linestyle='--')
# Labeling the axes
axes[2].set_xlabel('Nodes')
axes[2].set_ylabel('eigenvector')
# Display the plot
plt.show()
# Variance
variance_rho = np.var(last_values_rho)
variance_O = np.var(last_values_O)
variance_eigenvector = np.var(critical_eigenvector)
# Inverse Participation Ratio (IPR)
ipr_rho = np.sum(last_values_rho**4) / (np.sum(last_values_rho**2)**2)
ipr_O = np.sum(last_values_O**4) / (np.sum(last_values_O**2)**2)
ipr_eigenvector = np.sum(critical_eigenvector**4) / (np.sum(critical_eigenvector**2)**2)
# Network average degree
k_avg = 2 * e / n
print("Computations finished.")
# Return the results
return {
'critical_eigenvalue': float(eigenvalues[index_lambda_c]),
'last_values_rho': last_values_rho.tolist(),
'last_values_O': last_values_O.tolist(),
'critical_eigenvector': critical_eigenvector.tolist(),
'eigenvalues': eigenvalues.tolist(),
'variance_rho': float(variance_rho),
'variance_O': float(variance_O),
'variance_eigenvector': float(variance_eigenvector),
'ipr_rho': float(ipr_rho),
'ipr_O': float(ipr_O),
'ipr_eigenvector': float(ipr_eigenvector),
'k_avg': float(k_avg),
}
Experiments¶
In [6]:
# Create the experiments
def experiments(n_nodes, n_neighbors, n_experiments, sample_size, params):
print("Starting the experiments...")
transitivity = []
average_path_length = []
p_values = np.logspace(-4, 0, n_experiments)
small_world_graphs = []
# List that will contain the dynamics of the graphs
dynamics_data = {}
# Max clustering coefficient
max_clustering = 3/4 * (n_neighbors - 2) / (n_neighbors - 1)
# Max length
max_length = n_nodes / (2 * n_neighbors)
# Compute the transitivity and average length path for each graph
for i, p in enumerate(p_values):
print(f"Computing graph {i + 1}/{n_experiments}...")
small_world_graphs = []
transitivities = []
avg_lenghts = []
dynamics = []
print("Computing samples...")
for seed in range(sample_size):
small_world_graphs.append(nx.newman_watts_strogatz_graph(n=n_nodes, k=n_neighbors, p=p, seed=seed))
print("Computing dynamics...")
transitivities = list(map(lambda x: nx.transitivity(x) / max_clustering, small_world_graphs))
avg_lenghts = list(map(lambda x: nx.average_shortest_path_length(x) / max_length, small_world_graphs))
dynamics = list(map(lambda x: get_dynamics(x, params), small_world_graphs))
transitivity.append(np.mean(transitivities))
average_path_length.append(np.mean(avg_lenghts))
dynamics_data[p] = dynamics
# Save the data for each p
data_ipr_rho = sum([list(map(lambda x: x['ipr_rho'], dynamics_data[p])) for p in p_values], [])
data_ipr_O = sum([list(map(lambda x: x['ipr_O'], dynamics_data[p])) for p in p_values], [])
data_ipr_eigenvector = sum([list(map(lambda x: x['ipr_eigenvector'], dynamics_data[p])) for p in p_values], [])
data_variance_rho = sum([list(map(lambda x: x['variance_rho'], dynamics_data[p])) for p in p_values], [])
data_variance_O = sum([list(map(lambda x: x['variance_O'], dynamics_data[p])) for p in p_values], [])
data_variance_eigenvector = sum([list(map(lambda x: x['variance_eigenvector'], dynamics_data[p])) for p in p_values], [])
data_k_avg = sum([list(map(lambda x: x['k_avg'], dynamics_data[p])) for p in p_values], [])
data_p = sum([[p] * sample_size for p in p_values], [])
# Plot the results
print("Plotting the results...")
fig, axes = plt.subplots(5, 1, figsize=(10, 12))
# Plot transitivity and average path length
axes[0].plot(p_values, transitivity, label='Transitivity')
axes[0].plot(p_values, average_path_length, label='Average Path Length')
axes[0].set_xlabel('p')
axes[0].set_xscale('log')
axes[0].legend()
axes[0].set_title('Transitivity and Average Path Length')
axes[0].grid(True)
# Plot dynamics: IPR
axes[1].scatter(data_p, data_ipr_rho, label='IPR rho', alpha=0.7)
axes[1].scatter(data_p, data_ipr_O, label='IPR O', alpha=0.7)
axes[1].set_xlabel('p')
axes[1].set_xscale('log')
axes[1].legend()
axes[1].set_title('Dynamics: IPR')
axes[1].grid(True)
# Plot variance
axes[2].scatter(data_p, data_variance_rho, label='Variance rho', alpha=0.7)
axes[2].scatter(data_p, data_variance_O, label='Variance O', alpha=0.7)
axes[2].set_xlabel('p')
axes[2].set_xscale('log')
axes[2].legend()
axes[2].set_title('Variance')
axes[2].grid(True)
# Plot IPR eigenvector
axes[3].scatter(data_p, data_ipr_eigenvector, label='IPR eigenvector', alpha=0.7)
axes[3].set_xlabel('p')
axes[3].set_xscale('log')
axes[3].legend()
axes[3].set_title('IPR Eigenvector')
axes[3].grid(True)
# Plot variance eigenvector
axes[4].scatter(data_p, data_variance_eigenvector, label='Variance eigenvector', alpha=0.7)
axes[4].set_xlabel('p')
axes[4].set_xscale('log')
axes[4].legend()
axes[4].set_title('Variance Eigenvector')
axes[4].grid(True)
plt.tight_layout()
plt.show()
return {
"dynamics_data": dynamics_data,
"data_ipr_rho": data_ipr_rho,
"data_ipr_O": data_ipr_O,
"data_ipr_eigenvector": data_ipr_eigenvector,
"data_variance_rho": data_variance_rho,
"data_variance_O": data_variance_O,
"data_variance_eigenvector": data_variance_eigenvector,
"data_k_avg": data_k_avg
}
In [7]:
experiment = experiments(30, 6, 10, 2, params)
print(experiment)
Starting the experiments... Computing graph 1/10... Computing samples... Computing dynamics... Starting the integration... Integration finished. Linear algebra computations... Computations finished. Starting the integration... Integration finished. Linear algebra computations... Computations finished. Computing graph 2/10... Computing samples... Computing dynamics... Starting the integration... Integration finished. Linear algebra computations... Computations finished. Starting the integration... Integration finished. Linear algebra computations... Computations finished. Computing graph 3/10... Computing samples... Computing dynamics... Starting the integration... Integration finished. Linear algebra computations... Computations finished. Starting the integration... Integration finished. Linear algebra computations... Computations finished. Computing graph 4/10... Computing samples... Computing dynamics... Starting the integration... Integration finished. Linear algebra computations... Computations finished. Starting the integration... Integration finished. Linear algebra computations... Computations finished. Computing graph 5/10... Computing samples... Computing dynamics... Starting the integration... Integration finished. Linear algebra computations... Computations finished. Starting the integration... Integration finished. Linear algebra computations... Computations finished. Computing graph 6/10... Computing samples... Computing dynamics... Starting the integration... Integration finished. Linear algebra computations... Computations finished. Starting the integration... Integration finished. Linear algebra computations... Computations finished. Computing graph 7/10... Computing samples... Computing dynamics... Starting the integration... Integration finished. Linear algebra computations... Computations finished. Starting the integration... Integration finished. Linear algebra computations... Computations finished. Computing graph 8/10... Computing samples... Computing dynamics... Starting the integration... Integration finished. Linear algebra computations... Computations finished. Starting the integration... Integration finished. Linear algebra computations... Computations finished. Computing graph 9/10... Computing samples... Computing dynamics... Starting the integration... Integration finished. Linear algebra computations... Computations finished. Starting the integration... Integration finished. Linear algebra computations... Computations finished. Computing graph 10/10... Computing samples... Computing dynamics... Starting the integration... Integration finished. Linear algebra computations... Computations finished. Starting the integration... Integration finished. Linear algebra computations... Computations finished. Plotting the results...
{'dynamics_data': {np.float64(0.0001): [{'critical_eigenvalue': -2.2166138832471804, 'last_values_rho': [0.008069369484021295, 0.007757991823145214, 0.007793425361537228, 0.007848646375082624, 0.00780989513852471, 0.007910842841756038, 0.008021379685619084, 0.008095398401131403, 0.008191136477534697, 0.008217009270683206, 0.00818974370770322, 0.008087548342653987, 0.007922520014682726, 0.007845419749730924, 0.007639427228197823, 0.007451296886199155, 0.006811399902373398, 0.0056427017689586936, 0.007355472924916334, 0.007932542688189478, 0.007939240168919247, 0.007939501526918984, 0.007934794593733245, 0.007943088492244146, 0.007940227913686957, 0.007937463136890617, 0.00793674089393442, 0.0041482318525373554, 0.005807604486486839, 0.0069190259692731085], 'last_values_O': [0.6547344961459031, 0.6224460694396733, 0.6265632638216883, 0.6325340974268451, 0.6288520448208552, 0.6395144381491416, 0.6507461465356832, 0.6577757198745879, 0.6663127794936624, 0.6667269643972175, 0.6611952578592568, 0.6474986052385735, 0.6268898284572708, 0.6170037667518701, 0.5938887089899964, 0.5713386959357427, 0.5018836823072351, 0.3746958358646023, 0.5123677065827231, 0.6355728080343549, 0.6350081014428479, 0.6349870987914438, 0.6353755504226279, 0.6347024775252073, 0.6349289822788796, 0.6351524304587735, 0.6352119615281909, 0.2220301352213436, 0.40825445486338324, 0.5320480911525368], 'critical_eigenvector': [0.003512562286297117, -0.10180034588825296, -0.18951104943161556, -0.24445357087441705, -0.2571278491220584, -0.22534238632332013, -0.15459317775796771, -0.057113404323333526, 0.050241795577794665, 0.14890973259113857, 0.22182982403702273, 0.2563935236462212, 0.24662445375494937, 0.19421177529662195, 0.10821811653092007, 0.0035125622862969184, -0.10180034588825371, -0.18951104943161565, -0.24445357087441646, -0.25712784912205827, -0.22534238632331988, -0.1545931777579676, -0.057113404323333575, 0.050241795577794506, 0.14890973259113818, 0.2218298240370224, 0.2563935236462209, 0.24662445375494915, 0.19421177529662237, 0.10821811653091999], 'variance_rho': 7.799506021854283e-07, 'variance_O': 0.009702944906529684, 'variance_eigenvector': 0.033333333333333326, 'ipr_rho': 0.03463412649853244, 'ipr_O': 0.03564204343681443, 'ipr_eigenvector': 0.05000000000000001, 'k_avg': 6.0}, {'critical_eigenvalue': -2.2166138832471804, 'last_values_rho': [0.008069369484021295, 0.007757991823145214, 0.007793425361537228, 0.007848646375082624, 0.00780989513852471, 0.007910842841756038, 0.008021379685619084, 0.008095398401131403, 0.008191136477534697, 0.008217009270683206, 0.00818974370770322, 0.008087548342653987, 0.007922520014682726, 0.007845419749730924, 0.007639427228197823, 0.007451296886199155, 0.006811399902373398, 0.0056427017689586936, 0.007355472924916334, 0.007932542688189478, 0.007939240168919247, 0.007939501526918984, 0.007934794593733245, 0.007943088492244146, 0.007940227913686957, 0.007937463136890617, 0.00793674089393442, 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Experiments distributed¶
In [ ]:
from multiprocessing import Pool
def process_graph(args):
"""Helper function to process a single graph with given parameters"""
p, seed, n_nodes, n_neighbors, params = args
graph = nx.newman_watts_strogatz_graph(n=n_nodes, k=n_neighbors, p=p, seed=seed)
max_clustering = 3/4 * (n_neighbors - 2) / (n_neighbors - 1)
max_length = n_nodes / (2 * n_neighbors)
transitivity = nx.transitivity(graph) / max_clustering
avg_length = nx.average_shortest_path_length(graph) / max_length
dynamics = get_dynamics(graph, params)
# Compute the measures for the random erdos renyi graph
avg_degree = dynamics["k_avg"]
transitivity_random = (avg_degree / n_nodes) / max_clustering
avg_length_random = (np.log(n_nodes) / np.log(avg_degree)) / max_length
sigma = (transitivity / transitivity_random) / (avg_length / avg_length_random)
# Compute the presence of hubs
max_degree = max(dict(graph.degree()).values())
hub_ness = max_degree / avg_degree
return {
'transitivity': transitivity,
'avg_length': avg_length,
'dynamics': dynamics,
'sigma': sigma,
'hub_ness': hub_ness
}
def experiments(n_nodes, n_neighbors, n_experiments, sample_size, params):
print("Starting the experiments...")
transitivity = []
average_path_length = []
sigma_data = []
hub_data = []
p_values = np.logspace(-4, 0, n_experiments)
dynamics_data = {}
# Create process pool
with Pool() as pool:
for i, p in enumerate(p_values):
print(f"Computing graph {i + 1}/{n_experiments}...")
# Prepare arguments for parallel processing
args = [(p, seed, n_nodes, n_neighbors, params) for seed in range(sample_size)]
# Process graphs in parallel
results = pool.map(process_graph, args)
# Extract results
transitivities = [r['transitivity'] for r in results]
avg_lengths = [r['avg_length'] for r in results]
dynamics = [r['dynamics'] for r in results]
sigmas = [r['sigma'] for r in results]
hubs = [r['hub_ness'] for r in results]
transitivity.append(np.mean(transitivities))
average_path_length.append(np.mean(avg_lengths))
dynamics_data[p] = dynamics
# Save the mean of sigma
sigma_data.append(np.mean(sigmas))
# Save the mean of hub_ness
hub_data.append(np.mean(hubs))
# Rest of the code remains the same
data_ipr_rho = sum([list(map(lambda x: x['ipr_rho'], dynamics_data[p])) for p in p_values], [])
data_ipr_O = sum([list(map(lambda x: x['ipr_O'], dynamics_data[p])) for p in p_values], [])
data_ipr_eigenvector = sum([list(map(lambda x: x['ipr_eigenvector'], dynamics_data[p])) for p in p_values], [])
data_variance_rho = sum([list(map(lambda x: x['variance_rho'], dynamics_data[p])) for p in p_values], [])
data_variance_O = sum([list(map(lambda x: x['variance_O'], dynamics_data[p])) for p in p_values], [])
data_variance_eigenvector = sum([list(map(lambda x: x['variance_eigenvector'], dynamics_data[p])) for p in p_values], [])
data_k_avg = sum([list(map(lambda x: x['k_avg'], dynamics_data[p])) for p in p_values], [])
data_p = sum([[p] * sample_size for p in p_values], [])
# Plot the results
print("Plotting the results...")
fig, axes = plt.subplots(5, 1, figsize=(10, 12))
# Plot transitivity and average path length
axes[0].plot(p_values, transitivity, label='Transitivity')
axes[0].plot(p_values, average_path_length, label='Average Path Length')
# Plot vertical line for small world condition when True
axes[0].plot(p_values, sigma_data, label='Small-world-ness')
axes[0].plot(p_values, hub_data, label='Hub-ness')
axes[0].set_xlabel('p')
axes[0].set_xscale('log')
axes[0].legend()
axes[0].set_title('Transitivity and Average Path Length')
axes[0].grid(True)
# Plot dynamics: IPR
axes[1].scatter(data_p, data_ipr_rho, label='IPR rho', alpha=0.7)
axes[1].scatter(data_p, data_ipr_O, label='IPR O', alpha=0.7)
axes[1].set_xlabel('p')
axes[1].set_xscale('log')
axes[1].legend()
axes[1].set_title('Dynamics: IPR')
axes[1].grid(True)
# Plot variance
axes[2].scatter(data_p, data_variance_rho, label='Variance rho', alpha=0.7)
axes[2].scatter(data_p, data_variance_O, label='Variance O', alpha=0.7)
axes[2].set_xlabel('p')
axes[2].set_xscale('log')
axes[2].legend()
axes[2].set_title('Variance')
axes[2].grid(True)
# Plot IPR eigenvector
axes[3].scatter(data_p, data_ipr_eigenvector, label='IPR eigenvector', alpha=0.7)
axes[3].set_xlabel('p')
axes[3].set_xscale('log')
axes[3].legend()
axes[3].set_title('IPR Eigenvector')
axes[3].grid(True)
# Plot variance eigenvector
axes[4].scatter(data_p, data_variance_eigenvector, label='Variance eigenvector', alpha=0.7)
axes[4].set_xlabel('p')
axes[4].set_xscale('log')
axes[4].legend()
axes[4].set_title('Variance Eigenvector')
axes[4].grid(True)
plt.tight_layout()
plt.show()
return {
"dynamics_data": dynamics_data,
"data_ipr_rho": data_ipr_rho,
"data_ipr_O": data_ipr_O,
"data_ipr_eigenvector": data_ipr_eigenvector,
"data_variance_rho": data_variance_rho,
"data_variance_O": data_variance_O,
"data_variance_eigenvector": data_variance_eigenvector,
"data_k_avg": data_k_avg
}
Experiments distributed with box plots¶
In [23]:
from multiprocessing import Pool
def process_graph(args):
"""Helper function to process a single graph with given parameters"""
p, seed, n_nodes, n_neighbors, params = args
graph = nx.newman_watts_strogatz_graph(n=n_nodes, k=n_neighbors, p=p, seed=seed)
max_clustering = 3/4 * (n_neighbors - 2) / (n_neighbors - 1)
max_length = n_nodes / (2 * n_neighbors)
transitivity = nx.transitivity(graph) / max_clustering
avg_length = nx.average_shortest_path_length(graph) / max_length
dynamics = get_dynamics(graph, params)
# Compute the measures for the random erdos renyi graph
avg_degree = dynamics["k_avg"]
transitivity_random = (avg_degree / n_nodes) / max_clustering
avg_length_random = (np.log(n_nodes) / np.log(avg_degree)) / max_length
sigma = (transitivity / transitivity_random) / (avg_length / avg_length_random)
# Compute the presence of hubs
max_degree = max(dict(graph.degree()).values())
hub_ness = max_degree / avg_degree
return {
'transitivity': transitivity,
'avg_length': avg_length,
'dynamics': dynamics,
'sigma': sigma,
'hub_ness': hub_ness
}
def experiments(n_nodes, n_neighbors, n_experiments, sample_size, params):
print("Starting the experiments...")
transitivity = []
average_path_length = []
sigma_data = []
hub_data = []
p_values = np.logspace(-4, 0, n_experiments)
dynamics_data = {}
# Create process pool
with Pool() as pool:
for i, p in enumerate(p_values):
print(f"Computing graph {i + 1}/{n_experiments}...")
# Prepare arguments for parallel processing
args = [(p, seed, n_nodes, n_neighbors, params) for seed in range(sample_size)]
# Process graphs in parallel
results = pool.map(process_graph, args)
# Extract results
transitivities = [r['transitivity'] for r in results]
avg_lengths = [r['avg_length'] for r in results]
dynamics = [r['dynamics'] for r in results]
sigmas = [r['sigma'] for r in results]
hubs = [r['hub_ness'] for r in results]
transitivity.append(np.mean(transitivities))
average_path_length.append(np.mean(avg_lengths))
dynamics_data[p] = dynamics
# Save the mean of sigma
sigma_data.append(np.mean(sigmas))
# Save the mean of hub_ness
hub_data.append(np.mean(hubs))
# Rest of the code remains the same
data_ipr_rho = [list(map(lambda x: x['ipr_rho'], dynamics_data[p])) for p in p_values]
data_ipr_O = [list(map(lambda x: x['ipr_O'], dynamics_data[p])) for p in p_values]
data_ipr_eigenvector = [list(map(lambda x: x['ipr_eigenvector'], dynamics_data[p])) for p in p_values]
data_variance_rho = [list(map(lambda x: x['variance_rho'], dynamics_data[p])) for p in p_values]
data_variance_O = [list(map(lambda x: x['variance_O'], dynamics_data[p])) for p in p_values]
data_variance_eigenvector = [list(map(lambda x: x['variance_eigenvector'], dynamics_data[p])) for p in p_values]
data_k_avg = [list(map(lambda x: x['k_avg'], dynamics_data[p])) for p in p_values]
data_p = p_values
# Plot the results
print("Plotting the results...")
fig, axes = plt.subplots(5, 1, figsize=(10, 12))
# Plot transitivity and average path length
axes[0].plot(p_values, transitivity, label='Transitivity')
axes[0].plot(p_values, average_path_length, label='Average Path Length')
# Plot vertical line for small world condition when True
axes[0].plot(p_values, sigma_data, label='Small-world-ness')
axes[0].plot(p_values, hub_data, label='Hub-ness')
axes[0].set_xlabel('p')
axes[0].set_xscale('log')
axes[0].legend()
axes[0].set_title('Transitivity and Average Path Length')
axes[0].grid(True)
# Plot dynamics: IPR
widths = 0.1 * data_p
# Plot dynamics: IPR (rho and O)
for i, (x, y, w) in enumerate(zip(data_p, data_ipr_rho, widths)):
if i == 0:
axes[1].boxplot(y, positions=[x], widths=[w], label='IPR rho')
else:
axes[1].boxplot(y, positions=[x], widths=[w])
for i, (x, y, w) in enumerate(zip(data_p, data_ipr_O, widths)):
if i == 0:
axes[1].boxplot(y, positions=[x], widths=[w], label='IPR O')
else:
axes[1].boxplot(y, positions=[x], widths=[w])
axes[1].set_xlabel('p')
axes[1].set_xscale('log')
axes[1].legend()
axes[1].set_title('Dynamics: IPR')
axes[1].grid(True)
# Plot variance (rho and O) as boxplots
for i, (x, y, w) in enumerate(zip(data_p, data_variance_rho, widths)):
if i == 0:
axes[2].boxplot(y, positions=[x], widths=[w], label='Variance rho')
else:
axes[2].boxplot(y, positions=[x], widths=[w])
for i, (x, y, w) in enumerate(zip(data_p, data_variance_O, widths)):
if i == 0:
axes[2].boxplot(y, positions=[x], widths=[w], label='Variance O')
else:
axes[2].boxplot(y, positions=[x], widths=[w])
axes[2].set_xlabel('p')
axes[2].set_xscale('log')
axes[2].legend()
axes[2].set_title('Variance')
axes[2].grid(True)
# Plot IPR eigenvector as boxplots
for i, (x, y, w) in enumerate(zip(data_p, data_ipr_eigenvector, widths)):
if i == 0:
axes[3].boxplot(y, positions=[x], widths=[w], label='IPR eigenvector')
else:
axes[3].boxplot(y, positions=[x], widths=[w])
axes[3].set_xlabel('p')
axes[3].set_xscale('log')
axes[3].legend()
axes[3].set_title('IPR Eigenvector')
axes[3].grid(True)
# Plot variance eigenvector as boxplots
for i, (x, y, w) in enumerate(zip(data_p, data_variance_eigenvector, widths)):
if i == 0:
axes[4].boxplot(y, positions=[x], widths=[w], label='Variance eigenvector')
else:
axes[4].boxplot(y, positions=[x], widths=[w])
axes[4].set_xlabel('p')
axes[4].set_xscale('log')
axes[4].legend()
axes[4].set_title('Variance Eigenvector')
axes[4].grid(True)
plt.tight_layout()
plt.show()
return {
"dynamics_data": dynamics_data,
"data_ipr_rho": data_ipr_rho,
"data_ipr_O": data_ipr_O,
"data_ipr_eigenvector": data_ipr_eigenvector,
"data_variance_rho": data_variance_rho,
"data_variance_O": data_variance_O,
"data_variance_eigenvector": data_variance_eigenvector,
"data_k_avg": data_k_avg
}
In [24]:
experiment = experiments(16, 4, 50, 8, params)
print(experiment)
Starting the experiments... Starting the integration...Starting the integration...Starting the integration...Starting the integration...Starting the integration...Starting the integration...Starting the integration... Starting the integration... Computing graph 1/50... Integration finished.Integration finished.Integration finished. Linear algebra computations... Linear algebra computations...Linear algebra computations...Computations finished. Computations finished.Computations finished. Integration finished. Linear algebra computations... Integration finished. Linear algebra computations... Computations finished. Computations finished. Integration finished. Linear algebra computations... Computations finished. Integration finished. Linear algebra computations... Integration finished. Linear algebra computations...Computations finished. Computations finished. Starting the integration...Starting the integration...Starting the integration... Starting the integration... 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Starting the integration...Starting the integration...Starting the integration...Starting the integration...Starting the integration...Starting the integration...Starting the integration...Starting the integration... Computing graph 8/50... Integration finished. Integration finished.Linear algebra computations... Integration finished.Linear algebra computations... Linear algebra computations...Computations finished. Integration finished. Linear algebra computations... Computations finished. Computations finished. Integration finished.Computations finished. Linear algebra computations... Computations finished.Integration finished. Linear algebra computations... Computations finished.Integration finished. Integration finished.Linear algebra computations... Linear algebra computations... Computations finished. Computations finished. 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Integration finished.Linear algebra computations... Linear algebra computations...Integration finished. Computations finished.Linear algebra computations...Computations finished. Computations finished. Starting the integration...Starting the integration...Starting the integration...Starting the integration...Starting the integration...Starting the integration...Starting the integration...Starting the integration... Computing graph 19/50... Integration finished. Linear algebra computations... Computations finished. Integration finished. Linear algebra computations... Computations finished.Integration finished. Linear algebra computations... Computations finished. Integration finished. Linear algebra computations... Computations finished. Integration finished. Linear algebra computations...Integration finished. Linear algebra computations...Computations finished. Computations finished. Integration finished. Linear algebra computations... Computations finished.Integration finished. 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Integration finished. Linear algebra computations... Computations finished. Integration finished. Integration finished.Linear algebra computations... Linear algebra computations... Computations finished.Computations finished. Integration finished. Linear algebra computations... Computations finished. Starting the integration...Starting the integration...Starting the integration...Starting the integration...Starting the integration...Starting the integration...Starting the integration...Starting the integration... Computing graph 30/50... Integration finished. Linear algebra computations...Integration finished. Linear algebra computations...Computations finished. Computations finished. Integration finished. Linear algebra computations... Computations finished. Integration finished. Linear algebra computations... Computations finished. Integration finished. Linear algebra computations... Computations finished. Integration finished. Linear algebra computations... Computations finished. Integration finished. Linear algebra computations... Computations finished. Integration finished. Linear algebra computations... Computations finished. Starting the integration...Starting the integration...Starting the integration...Starting the integration...Starting the integration...Starting the integration... Starting the integration... Starting the integration... Computing graph 31/50... Integration finished. Linear algebra computations... Computations finished. Integration finished. Linear algebra computations... Computations finished. Integration finished. Linear algebra computations... Computations finished. Integration finished. Linear algebra computations... Computations finished. Integration finished.Integration finished. Linear algebra computations...Linear algebra computations... Computations finished.Computations finished. Integration finished. Linear algebra computations... Computations finished. Integration finished. Linear algebra computations... Computations finished. Starting the integration...Starting the integration...Starting the integration...Starting the integration...Starting the integration...Starting the integration...Starting the integration... Starting the integration... Computing graph 32/50... Integration finished. Linear algebra computations... Computations finished. Integration finished. Linear algebra computations... Computations finished. Integration finished. Linear algebra computations... Computations finished. Integration finished. Linear algebra computations... Computations finished. Integration finished. Linear algebra computations... Computations finished. Integration finished. Linear algebra computations... Computations finished. Integration finished. Linear algebra computations... Computations finished.Integration finished. Linear algebra computations... Computations finished. Starting the integration...Starting the integration...Starting the integration...Starting the integration...Starting the integration...Starting the integration...Starting the integration...Starting the integration... Computing graph 33/50... Integration finished. Linear algebra computations... Computations finished. Integration finished. Linear algebra computations... Computations finished. Integration finished. Linear algebra computations... Computations finished. Integration finished. Linear algebra computations... Computations finished.Integration finished. Linear algebra computations... Integration finished.Computations finished. Linear algebra computations... Integration finished.Computations finished. Linear algebra computations... Computations finished. Integration finished. Linear algebra computations... Computations finished. Starting the integration...Starting the integration...Starting the integration...Starting the integration...Starting the integration...Starting the integration...Starting the integration... Starting the integration... Computing graph 34/50... Integration finished. Linear algebra computations... Integration finished. Linear algebra computations...Computations finished. Integration finished. Computations finished.Linear algebra computations... Computations finished. Integration finished. Linear algebra computations... Computations finished. Integration finished. Linear algebra computations... Computations finished. Integration finished. Linear algebra computations... Computations finished. Integration finished. Linear algebra computations... Computations finished. Integration finished. Linear algebra computations... Computations finished. Starting the integration...Starting the integration...Starting the integration...Starting the integration...Starting the integration...Starting the integration...Starting the integration...Starting the integration... Computing graph 35/50... Integration finished. Linear algebra computations...Integration finished. Linear algebra computations...Computations finished. Computations finished. Integration finished. Linear algebra computations... Computations finished. Integration finished. Linear algebra computations... Computations finished. Integration finished. Linear algebra computations... Computations finished. Integration finished. Linear algebra computations... Computations finished. Integration finished. Linear algebra computations... Integration finished. Computations finished.Linear algebra computations... Computations finished. Starting the integration...Starting the integration...Starting the integration...Starting the integration...Starting the integration...Starting the integration...Starting the integration... Starting the integration... Computing graph 36/50... Integration finished. Integration finished.Linear algebra computations... Linear algebra computations...Computations finished. Computations finished. Integration finished. Linear algebra computations... Computations finished. Integration finished. Linear algebra computations... Computations finished.Integration finished. Linear algebra computations... Computations finished. Integration finished. Linear algebra computations... Computations finished. Integration finished.Integration finished. Linear algebra computations...Linear algebra computations... Computations finished.Computations finished. Starting the integration...Starting the integration...Starting the integration...Starting the integration...Starting the integration...Starting the integration... Starting the integration...Starting the integration... Computing graph 37/50... Integration finished. Linear algebra computations... Computations finished. Integration finished. Linear algebra computations... Integration finished. Computations finished.Linear algebra computations... Computations finished. Integration finished.Integration finished. Linear algebra computations...Linear algebra computations... Integration finished.Computations finished. Integration finished.Computations finished. Linear algebra computations...Linear algebra computations... Computations finished.Computations finished. Integration finished. Linear algebra computations... Computations finished. Starting the integration...Starting the integration...Starting the integration...Starting the integration...Starting the integration...Starting the integration...Starting the integration... Starting the integration... Computing graph 38/50... Integration finished. Linear algebra computations... Computations finished. Integration finished. Linear algebra computations... Computations finished. Integration finished.Integration finished. Linear algebra computations...Linear algebra computations... Computations finished.Computations finished. Integration finished. Linear algebra computations... Computations finished. Integration finished.Integration finished. Linear algebra computations...Linear algebra computations... Computations finished.Computations finished. Integration finished. Linear algebra computations... Computations finished. Starting the integration...Starting the integration...Starting the integration...Starting the integration...Starting the integration...Starting the integration...Starting the integration... Starting the integration... Computing graph 39/50... Integration finished. Linear algebra computations... Computations finished. Integration finished. Linear algebra computations... Integration finished. Computations finished.Linear algebra computations... Computations finished. Integration finished. Linear algebra computations... Integration finished.Computations finished. Linear algebra computations... Computations finished. Integration finished. Linear algebra computations... Computations finished. Integration finished. Linear algebra computations... Computations finished. Integration finished. Linear algebra computations... Computations finished. Starting the integration...Starting the integration...Starting the integration...Starting the integration...Starting the integration...Starting the integration...Starting the integration... Starting the integration... Computing graph 40/50... Integration finished. Linear algebra computations... Computations finished. Integration finished. Linear algebra computations...Integration finished. Linear algebra computations...Computations finished. Computations finished. Integration finished. Linear algebra computations... Computations finished. Integration finished. Linear algebra computations... Computations finished. Integration finished. Linear algebra computations...Integration finished. Linear algebra computations... Computations finished. Computations finished. Integration finished. Linear algebra computations... Computations finished. Starting the integration...Starting the integration...Starting the integration...Starting the integration...Starting the integration...Starting the integration...Starting the integration...Starting the integration... Computing graph 41/50... Integration finished. Linear algebra computations... Computations finished.Integration finished. Linear algebra computations... Integration finished.Computations finished. Linear algebra computations... Computations finished. Integration finished. Linear algebra computations... Computations finished. Integration finished. Linear algebra computations... Computations finished.Integration finished.Integration finished. Linear algebra computations...Linear algebra computations... Computations finished.Computations finished. Integration finished. Linear algebra computations... Computations finished. Starting the integration...Starting the integration...Starting the integration...Starting the integration...Starting the integration...Starting the integration...Starting the integration...Starting the integration... Computing graph 42/50... Integration finished. Linear algebra computations... Computations finished. Integration finished. Linear algebra computations... Computations finished. Integration finished. Linear algebra computations...Integration finished. Linear algebra computations...Computations finished. Integration finished.Computations finished. Linear algebra computations... Computations finished. Integration finished.Integration finished. Linear algebra computations...Linear algebra computations... Computations finished.Computations finished.Integration finished. Linear algebra computations... Computations finished. Starting the integration...Starting the integration...Starting the integration...Starting the integration...Starting the integration...Starting the integration...Starting the integration... Starting the integration... Computing graph 43/50... Integration finished. Linear algebra computations... Integration finished. Linear algebra computations...Computations finished. Integration finished. Computations finished. Linear algebra computations... Computations finished. Integration finished.Integration finished. Linear algebra computations...Linear algebra computations... Computations finished.Computations finished. Integration finished. Linear algebra computations... Computations finished. Integration finished. Linear algebra computations...Integration finished. Linear algebra computations... Computations finished. Computations finished. Starting the integration...Starting the integration...Starting the integration...Starting the integration...Starting the integration...Starting the integration...Starting the integration... Starting the integration... Computing graph 44/50... Integration finished. Linear algebra computations... Computations finished. Integration finished.Integration finished. Linear algebra computations...Linear algebra computations... Computations finished.Computations finished. Integration finished. Linear algebra computations... Computations finished. Integration finished. Linear algebra computations... Computations finished.Integration finished. Linear algebra computations... Computations finished. Integration finished. Linear algebra computations... Computations finished. Integration finished. Linear algebra computations... Computations finished. Starting the integration...Starting the integration...Starting the integration...Starting the integration...Starting the integration...Starting the integration...Starting the integration... Starting the integration... Computing graph 45/50... Integration finished. Linear algebra computations... Computations finished. Integration finished. Linear algebra computations... Computations finished. Integration finished.Integration finished. Integration finished.Linear algebra computations... Linear algebra computations... Linear algebra computations... Computations finished. Computations finished.Computations finished. Integration finished.Integration finished. Linear algebra computations...Linear algebra computations... Computations finished.Computations finished. Integration finished. Linear algebra computations... Computations finished. Starting the integration...Starting the integration...Starting the integration...Starting the integration...Starting the integration...Starting the integration...Starting the integration...Starting the integration... Computing graph 46/50... Integration finished. Linear algebra computations... Integration finished.Computations finished. Linear algebra computations... Computations finished. Integration finished. Linear algebra computations... Computations finished.Integration finished. Linear algebra computations... The critical eigenvalue is not in the range of the dispersion relation. The linear analysis cannot be performed. The critical eigenvalue is: -2.6522442301296834 Integration finished.
/tmp/ipykernel_1027/3001995589.py:147: RuntimeWarning: invalid value encountered in scalar divide ipr_eigenvector = np.sum(critical_eigenvector**4) / (np.sum(critical_eigenvector**2)**2)
Computations finished.Linear algebra computations... Computations finished.Integration finished. Linear algebra computations... The critical eigenvalue is not in the range of the dispersion relation. The linear analysis cannot be performed. The critical eigenvalue is: Integration finished. -2.4908803515668563 Integration finished. Linear algebra computations...
/tmp/ipykernel_1027/3001995589.py:147: RuntimeWarning: invalid value encountered in scalar divide ipr_eigenvector = np.sum(critical_eigenvector**4) / (np.sum(critical_eigenvector**2)**2)
Linear algebra computations...Computations finished. Computations finished. Computations finished. Starting the integration...Starting the integration...Starting the integration...Starting the integration...Starting the integration...Starting the integration...Starting the integration...Starting the integration... Computing graph 47/50... Integration finished. Linear algebra computations... The critical eigenvalue is not in the range of the dispersion relation. The linear analysis cannot be performed. The critical eigenvalue is: -1.7763568394002505e-15
/tmp/ipykernel_1027/3001995589.py:147: RuntimeWarning: invalid value encountered in scalar divide ipr_eigenvector = np.sum(critical_eigenvector**4) / (np.sum(critical_eigenvector**2)**2)
Computations finished. Integration finished. Linear algebra computations... Computations finished. Integration finished. Linear algebra computations... Integration finished. Linear algebra computations...Computations finished. The critical eigenvalue is not in the range of the dispersion relation. The linear analysis cannot be performed. The critical eigenvalue is: Integration finished. -1.7763568394002505e-15Linear algebra computations...
/tmp/ipykernel_1027/3001995589.py:147: RuntimeWarning: invalid value encountered in scalar divide ipr_eigenvector = np.sum(critical_eigenvector**4) / (np.sum(critical_eigenvector**2)**2)
Computations finished.Computations finished. Integration finished. Linear algebra computations... Computations finished. Integration finished. Linear algebra computations... The critical eigenvalue is not in the range of the dispersion relation. The linear analysis cannot be performed. The critical eigenvalue is: -2.6896803071991684 Computations finished. Integration finished. Linear algebra computations... The critical eigenvalue is not in the range of the dispersion relation. The linear analysis cannot be performed. The critical eigenvalue is: -2.829489310684999
/tmp/ipykernel_1027/3001995589.py:147: RuntimeWarning: invalid value encountered in scalar divide ipr_eigenvector = np.sum(critical_eigenvector**4) / (np.sum(critical_eigenvector**2)**2)
Computations finished. Starting the integration...Starting the integration...Starting the integration...Starting the integration...Starting the integration...Starting the integration...Starting the integration...Starting the integration... Computing graph 48/50... Integration finished. Linear algebra computations... The critical eigenvalue is not in the range of the dispersion relation. The linear analysis cannot be performed. The critical eigenvalue is: 0.0
/tmp/ipykernel_1027/3001995589.py:147: RuntimeWarning: invalid value encountered in scalar divide ipr_eigenvector = np.sum(critical_eigenvector**4) / (np.sum(critical_eigenvector**2)**2)
Computations finished. Integration finished. Integration finished. Linear algebra computations...Linear algebra computations... The critical eigenvalue is not in the range of the dispersion relation.The critical eigenvalue is not in the range of the dispersion relation. The linear analysis cannot be performed.The linear analysis cannot be performed. The critical eigenvalue is: The critical eigenvalue is: Integration finished. -1.7763568394002505e-150.0 Linear algebra computations...Computations finished.
/tmp/ipykernel_1027/3001995589.py:147: RuntimeWarning: invalid value encountered in scalar divide ipr_eigenvector = np.sum(critical_eigenvector**4) / (np.sum(critical_eigenvector**2)**2)
Computations finished. The critical eigenvalue is not in the range of the dispersion relation. The linear analysis cannot be performed. The critical eigenvalue is: Integration finished. 8.881784197001252e-16Linear algebra computations... Integration finished.
/tmp/ipykernel_1027/3001995589.py:147: RuntimeWarning: invalid value encountered in scalar divide ipr_eigenvector = np.sum(critical_eigenvector**4) / (np.sum(critical_eigenvector**2)**2)
Computations finished.The critical eigenvalue is not in the range of the dispersion relation.Linear algebra computations... The linear analysis cannot be performed. The critical eigenvalue is: Computations finished.Integration finished. -3.552713678800501e-15Linear algebra computations... Computations finished. The critical eigenvalue is not in the range of the dispersion relation. The linear analysis cannot be performed. The critical eigenvalue is: -2.6645352591003757e-15
/tmp/ipykernel_1027/3001995589.py:147: RuntimeWarning: invalid value encountered in scalar divide ipr_eigenvector = np.sum(critical_eigenvector**4) / (np.sum(critical_eigenvector**2)**2)
Computations finished. Integration finished. Linear algebra computations... The critical eigenvalue is not in the range of the dispersion relation. The linear analysis cannot be performed. The critical eigenvalue is: 0.0 Computations finished. Starting the integration...Starting the integration...Starting the integration...Starting the integration...Starting the integration...Starting the integration... Starting the integration...Starting the integration... Computing graph 49/50... Integration finished. Linear algebra computations... The critical eigenvalue is not in the range of the dispersion relation. The linear analysis cannot be performed. The critical eigenvalue is: 4.440892098500626e-16
/tmp/ipykernel_1027/3001995589.py:147: RuntimeWarning: invalid value encountered in scalar divide ipr_eigenvector = np.sum(critical_eigenvector**4) / (np.sum(critical_eigenvector**2)**2)
Computations finished. Integration finished. Linear algebra computations... The critical eigenvalue is not in the range of the dispersion relation. The linear analysis cannot be performed. The critical eigenvalue is: 3.552713678800501e-15Integration finished. Linear algebra computations...Computations finished. The critical eigenvalue is not in the range of the dispersion relation. The linear analysis cannot be performed. The critical eigenvalue is: 7.105427357601002e-15 Computations finished. Integration finished. Linear algebra computations... The critical eigenvalue is not in the range of the dispersion relation. The linear analysis cannot be performed. The critical eigenvalue is: -4.440892098500626e-16 Computations finished. Integration finished. Linear algebra computations... Integration finished. The critical eigenvalue is not in the range of the dispersion relation.Linear algebra computations... The linear analysis cannot be performed. The critical eigenvalue is not in the range of the dispersion relation.The critical eigenvalue is: The linear analysis cannot be performed.-1.7763568394002505e-15 The critical eigenvalue is: Computations finished. -8.881784197001252e-16 Computations finished. Integration finished. Linear algebra computations... The critical eigenvalue is not in the range of the dispersion relation. The linear analysis cannot be performed. The critical eigenvalue is: -3.552713678800501e-15 Computations finished. Integration finished. Linear algebra computations... The critical eigenvalue is not in the range of the dispersion relation. The linear analysis cannot be performed. The critical eigenvalue is: -1.5670163022740397e-15
/tmp/ipykernel_1027/3001995589.py:147: RuntimeWarning: invalid value encountered in scalar divide ipr_eigenvector = np.sum(critical_eigenvector**4) / (np.sum(critical_eigenvector**2)**2)
Computations finished. Starting the integration...Starting the integration...Starting the integration...Starting the integration...Starting the integration...Starting the integration...Starting the integration...Starting the integration... Computing graph 50/50... Integration finished. Linear algebra computations... The critical eigenvalue is not in the range of the dispersion relation. Integration finished.The linear analysis cannot be performed. Linear algebra computations... The critical eigenvalue is: The critical eigenvalue is not in the range of the dispersion relation.2.6645352591003757e-15 Computations finished.The linear analysis cannot be performed. The critical eigenvalue is: 0.0Integration finished. Computations finished.Linear algebra computations... The critical eigenvalue is not in the range of the dispersion relation. The linear analysis cannot be performed. The critical eigenvalue is: 0.0 Computations finished. Integration finished. Linear algebra computations... The critical eigenvalue is not in the range of the dispersion relation. The linear analysis cannot be performed. The critical eigenvalue is: 0.0 Computations finished. Integration finished. Linear algebra computations... Integration finished.The critical eigenvalue is not in the range of the dispersion relation. Linear algebra computations...The linear analysis cannot be performed. The critical eigenvalue is: The critical eigenvalue is not in the range of the dispersion relation. 5.329070518200751e-15The linear analysis cannot be performed. Computations finished.The critical eigenvalue is: 1.7763568394002505e-15 Integration finished.Computations finished. Linear algebra computations...Integration finished. Linear algebra computations...The critical eigenvalue is not in the range of the dispersion relation. The linear analysis cannot be performed.The critical eigenvalue is not in the range of the dispersion relation. The critical eigenvalue is: The linear analysis cannot be performed. 1.7763568394002505e-15The critical eigenvalue is: Computations finished.0.0
/tmp/ipykernel_1027/3001995589.py:147: RuntimeWarning: invalid value encountered in scalar divide ipr_eigenvector = np.sum(critical_eigenvector**4) / (np.sum(critical_eigenvector**2)**2)
Computations finished. Plotting the results...
{'dynamics_data': {np.float64(0.0001): [{'critical_eigenvalue': -0.7380273726043328, 'last_values_rho': [0.00786738013915125, 0.007993557357397, 0.008030877697298544, 0.008025246411075843, 0.007927773800330138, 0.007820442468506, 0.007799985372662481, 0.0078112770961355, 0.007957020378756414, 0.008058110634471835, 0.008127938333178535, 0.008093816791087451, 0.007962580175752264, 0.007867840398784083, 0.007766180474003875, 0.0078119832204089626], 'last_values_O': [0.6168204847199908, 0.6333117755557852, 0.6387323683356633, 0.6386175433047406, 0.6266288290984391, 0.6143722943269092, 0.6151782311682502, 0.6218269064730495, 0.6472657934025864, 0.6659615298673007, 0.6775935740956797, 0.6708991662434024, 0.6477252780395314, 0.6285368356504086, 0.609276841611744, 0.6114096776779269], 'critical_eigenvector': [0.353553390593274, 0.3266407412190944, 0.25000000000000017, 0.13529902503654953, 2.1134449387539346e-16, -0.13529902503654886, -0.2499999999999998, -0.32664074121909387, -0.3535533905932736, -0.32664074121909387, -0.25000000000000017, -0.13529902503654906, -7.65615853667037e-18, 0.13529902503654936, 0.25000000000000017, 0.32664074121909425], 'eigenvalues': [1.1102230246251565e-16, -0.7380273726043328, -3.9999999999999836, -0.7380273726043307, -2.5857864376269095, -2.5857864376269095, -4.433545502649473, -4.4335455026494826, -4.648846697642915, -4.64884669764292, -6.179580427103273, -6.179580427103271, -5.999999999999994, -6.000000000000004, -5.414213562373096, -5.414213562373092], 'variance_rho': 1.2434590518624294e-08, 'variance_O': 0.0004409507318121742, 'variance_eigenvector': 0.0625, 'ipr_rho': 0.06254948283070734, 'ipr_O': 0.0627784941737957, 'ipr_eigenvector': 0.09375000000000003, 'k_avg': 4.0}, {'critical_eigenvalue': -0.7380273726043328, 'last_values_rho': [0.00786738013915125, 0.007993557357397, 0.008030877697298544, 0.008025246411075843, 0.007927773800330138, 0.007820442468506, 0.007799985372662481, 0.0078112770961355, 0.007957020378756414, 0.008058110634471835, 0.008127938333178535, 0.008093816791087451, 0.007962580175752264, 0.007867840398784083, 0.007766180474003875, 0.0078119832204089626], 'last_values_O': [0.6168204847199908, 0.6333117755557852, 0.6387323683356633, 0.6386175433047406, 0.6266288290984391, 0.6143722943269092, 0.6151782311682502, 0.6218269064730495, 0.6472657934025864, 0.6659615298673007, 0.6775935740956797, 0.6708991662434024, 0.6477252780395314, 0.6285368356504086, 0.609276841611744, 0.6114096776779269], 'critical_eigenvector': [0.353553390593274, 0.3266407412190944, 0.25000000000000017, 0.13529902503654953, 2.1134449387539346e-16, -0.13529902503654886, -0.2499999999999998, -0.32664074121909387, -0.3535533905932736, -0.32664074121909387, -0.25000000000000017, -0.13529902503654906, -7.65615853667037e-18, 0.13529902503654936, 0.25000000000000017, 0.32664074121909425], 'eigenvalues': [1.1102230246251565e-16, -0.7380273726043328, -3.9999999999999836, -0.7380273726043307, -2.5857864376269095, -2.5857864376269095, -4.433545502649473, -4.4335455026494826, -4.648846697642915, -4.64884669764292, -6.179580427103273, -6.179580427103271, -5.999999999999994, -6.000000000000004, -5.414213562373096, -5.414213562373092], 'variance_rho': 1.2434590518624294e-08, 'variance_O': 0.0004409507318121742, 'variance_eigenvector': 0.0625, 'ipr_rho': 0.06254948283070734, 'ipr_O': 0.0627784941737957, 'ipr_eigenvector': 0.09375000000000003, 'k_avg': 4.0}, {'critical_eigenvalue': -0.7380273726043328, 'last_values_rho': [0.00786738013915125, 0.007993557357397, 0.008030877697298544, 0.008025246411075843, 0.007927773800330138, 0.007820442468506, 0.007799985372662481, 0.0078112770961355, 0.007957020378756414, 0.008058110634471835, 0.008127938333178535, 0.008093816791087451, 0.007962580175752264, 0.007867840398784083, 0.007766180474003875, 0.0078119832204089626], 'last_values_O': [0.6168204847199908, 0.6333117755557852, 0.6387323683356633, 0.6386175433047406, 0.6266288290984391, 0.6143722943269092, 0.6151782311682502, 0.6218269064730495, 0.6472657934025864, 0.6659615298673007, 0.6775935740956797, 0.6708991662434024, 0.6477252780395314, 0.6285368356504086, 0.609276841611744, 0.6114096776779269], 'critical_eigenvector': [0.353553390593274, 0.3266407412190944, 0.25000000000000017, 0.13529902503654953, 2.1134449387539346e-16, -0.13529902503654886, -0.2499999999999998, -0.32664074121909387, -0.3535533905932736, -0.32664074121909387, -0.25000000000000017, -0.13529902503654906, -7.65615853667037e-18, 0.13529902503654936, 0.25000000000000017, 0.32664074121909425], 'eigenvalues': [1.1102230246251565e-16, -0.7380273726043328, -3.9999999999999836, -0.7380273726043307, -2.5857864376269095, -2.5857864376269095, -4.433545502649473, -4.4335455026494826, -4.648846697642915, -4.64884669764292, -6.179580427103273, -6.179580427103271, -5.999999999999994, -6.000000000000004, -5.414213562373096, -5.414213562373092], 'variance_rho': 1.2434590518624294e-08, 'variance_O': 0.0004409507318121742, 'variance_eigenvector': 0.0625, 'ipr_rho': 0.06254948283070734, 'ipr_O': 0.0627784941737957, 'ipr_eigenvector': 0.09375000000000003, 'k_avg': 4.0}, {'critical_eigenvalue': -0.7380273726043328, 'last_values_rho': [0.00786738013915125, 0.007993557357397, 0.008030877697298544, 0.008025246411075843, 0.007927773800330138, 0.007820442468506, 0.007799985372662481, 0.0078112770961355, 0.007957020378756414, 0.008058110634471835, 0.008127938333178535, 0.008093816791087451, 0.007962580175752264, 0.007867840398784083, 0.007766180474003875, 0.0078119832204089626], 'last_values_O': [0.6168204847199908, 0.6333117755557852, 0.6387323683356633, 0.6386175433047406, 0.6266288290984391, 0.6143722943269092, 0.6151782311682502, 0.6218269064730495, 0.6472657934025864, 0.6659615298673007, 0.6775935740956797, 0.6708991662434024, 0.6477252780395314, 0.6285368356504086, 0.609276841611744, 0.6114096776779269], 'critical_eigenvector': [0.353553390593274, 0.3266407412190944, 0.25000000000000017, 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4.0], [4.0, 4.0, 4.0, 4.0, 4.0, 4.0, 4.0, 4.0], [4.0, 4.0, 4.0, 4.0, 4.0, 4.0, 4.0, 4.0], [4.0, 4.0, 4.0, 4.0, 4.0, 4.0, 4.0, 4.0], [4.0, 4.0, 4.0, 4.0, 4.0, 4.0, 4.0, 4.0], [4.0, 4.0, 4.0, 4.0, 4.0, 4.0, 4.0, 4.0], [4.0, 4.0, 4.0, 4.0, 4.0, 4.0, 4.0, 4.0], [4.0, 4.0, 4.0, 4.0, 4.0, 4.0, 4.125, 4.0], [4.0, 4.0, 4.0, 4.0, 4.0, 4.0, 4.125, 4.0], [4.0, 4.0, 4.0, 4.0, 4.0, 4.0, 4.125, 4.0], [4.0, 4.0, 4.0, 4.0, 4.0, 4.0, 4.125, 4.0], [4.0, 4.0, 4.0, 4.0, 4.0, 4.0, 4.125, 4.0], [4.0, 4.0, 4.0, 4.0, 4.0, 4.0, 4.125, 4.0], [4.0, 4.0, 4.0, 4.0, 4.0, 4.0, 4.125, 4.0], [4.0, 4.0, 4.0, 4.0, 4.0, 4.125, 4.125, 4.0], [4.0, 4.125, 4.0, 4.0, 4.0, 4.125, 4.125, 4.0], [4.0, 4.125, 4.0, 4.0, 4.0, 4.125, 4.125, 4.0], [4.0, 4.125, 4.0, 4.0, 4.0, 4.125, 4.125, 4.0], [4.0, 4.125, 4.0, 4.0, 4.0, 4.125, 4.125, 4.0], [4.0, 4.125, 4.0, 4.0, 4.0, 4.125, 4.125, 4.0], [4.0, 4.125, 4.0, 4.0, 4.0, 4.125, 4.125, 4.0], [4.0, 4.125, 4.0, 4.0, 4.0, 4.125, 4.125, 4.0], [4.0, 4.125, 4.0, 4.0, 4.0, 4.125, 4.125, 4.0], [4.0, 4.25, 4.0, 4.0, 4.0, 4.125, 4.125, 4.0], [4.0, 4.25, 4.0, 4.125, 4.0, 4.25, 4.125, 4.0], [4.0, 4.25, 4.0, 4.25, 4.0, 4.25, 4.125, 4.0], [4.0, 4.25, 4.0, 4.25, 4.0, 4.25, 4.125, 4.0], [4.0, 4.25, 4.0, 4.25, 4.0, 4.25, 4.25, 4.0], [4.0, 4.25, 4.125, 4.25, 4.0, 4.25, 4.25, 4.0], [4.0, 4.5, 4.125, 4.25, 4.0, 4.25, 4.25, 4.0], [4.0, 4.5, 4.125, 4.25, 4.0, 4.25, 4.25, 4.125], [4.0, 4.5, 4.125, 4.375, 4.0, 4.25, 4.25, 4.125], [4.0, 4.5, 4.25, 4.375, 4.0, 4.5, 4.25, 4.5], [4.0, 4.5, 4.25, 4.375, 4.25, 4.5, 4.25, 4.625], [4.0, 4.5, 4.25, 4.375, 4.375, 4.5, 4.25, 4.75], [4.125, 4.625, 4.25, 4.375, 4.5, 4.5, 4.625, 5.0], [4.125, 4.625, 4.25, 4.375, 4.75, 4.5, 4.625, 5.0], [4.125, 5.0, 4.25, 4.75, 4.75, 4.75, 4.625, 5.125], [4.125, 5.0, 4.625, 4.75, 4.75, 5.0, 4.625, 5.375], [4.125, 5.0, 4.625, 5.0, 4.875, 5.125, 5.0, 5.375], [5.0, 5.125, 4.5, 5.0, 5.5, 5.375, 4.75, 5.375], [5.125, 5.125, 4.75, 5.0, 5.5, 5.75, 5.0, 5.375], [5.5, 5.125, 5.25, 5.125, 5.5, 5.875, 5.25, 5.5], [5.375, 5.5, 5.25, 5.375, 6.125, 5.875, 5.375, 6.375], [6.5, 6.25, 5.625, 5.75, 6.625, 6.0, 6.25, 6.75], [6.75, 6.75, 6.0, 6.375, 7.0, 6.625, 7.0, 7.125], [7.125, 7.375, 7.125, 7.5, 7.625, 7.375, 7.625, 7.625], [8.0, 8.0, 8.0, 8.0, 8.0, 8.0, 8.0, 8.0]]}
In [23]:
experiment_2 = experiments(25, 6, 50, 8, params)
print(experiment_2)
Starting the experiments... Starting the integration...Starting the integration...Starting the integration...Starting the integration...Starting the integration...Starting the integration...Starting the integration...Starting the integration... Computing graph 1/50... Integration finished. Linear algebra computations... Integration finished. Computations finished.Linear algebra computations... Integration finished.Computations finished. Linear algebra computations... Computations finished. Integration finished. Linear algebra computations... Computations finished. Integration finished. Linear algebra computations... Computations finished. Integration finished. Linear algebra computations... Computations finished. Integration finished. Linear algebra computations... Integration finished. Computations finished.Linear algebra computations... Computations finished. Starting the integration...Starting the integration... Starting the integration...Starting the integration... Starting the integration...Starting the integration...Starting the integration...Starting the integration... Computing graph 2/50... Integration finished. Integration finished.Linear algebra computations... Linear algebra computations... Computations finished. Computations finished. Integration finished. Linear algebra computations... Computations finished. Integration finished. Linear algebra computations... Integration finished.Computations finished. Linear algebra computations... Computations finished.Integration finished. Linear algebra computations... Computations finished. Integration finished. Integration finished.Linear algebra computations... Linear algebra computations... Computations finished. Computations finished. Starting the integration...Starting the integration...Starting the integration...Starting the integration...Starting the integration...Starting the integration... Starting the integration... Starting the integration... Computing graph 3/50... Integration finished. Linear algebra computations... Computations finished. Integration finished. Linear algebra computations... Computations finished. Integration finished. Linear algebra computations... Computations finished. Integration finished. Linear algebra computations... Computations finished. Integration finished. Linear algebra computations... Computations finished. Integration finished. Linear algebra computations... Computations finished. Integration finished. Linear algebra computations... Integration finished.Computations finished. Linear algebra computations... Computations finished. Starting the integration...Starting the integration...Starting the integration...Starting the integration...Starting the integration...Starting the integration...Starting the integration...Starting the integration... Computing graph 4/50... Integration finished. Linear algebra computations... Computations finished. Integration finished. Linear algebra computations... Computations finished. Integration finished. Linear algebra computations... Integration finished. Computations finished.Integration finished.Linear algebra computations... Linear algebra computations... Computations finished. Computations finished. Integration finished. Integration finished.Linear algebra computations... Linear algebra computations... Computations finished. Computations finished. Integration finished. Linear algebra computations... Computations finished. Starting the integration...Starting the integration...Starting the integration...Starting the integration...Starting the integration...Starting the integration...Starting the integration...Starting the integration... Computing graph 5/50... Integration finished.Integration finished. Linear algebra computations...Linear algebra computations... Computations finished. Computations finished. Integration finished.Integration finished. Linear algebra computations...Linear algebra computations... Computations finished.Computations finished. Integration finished. Linear algebra computations... Computations finished. Integration finished. Integration finished.Linear algebra computations... Integration finished. Linear algebra computations... Linear algebra computations... Computations finished.Computations finished. Computations finished. Starting the integration...Starting the integration...Starting the integration...Starting the integration...Starting the integration...Starting the integration...Starting the integration...Starting the integration... Computing graph 6/50... Integration finished. Linear algebra computations... Integration finished. Linear algebra computations...Computations finished.Integration finished. Computations finished.Linear algebra computations... Computations finished. Integration finished. Linear algebra computations... Computations finished. Integration finished. Linear algebra computations... Computations finished. Integration finished. Linear algebra computations... Computations finished. Integration finished. Linear algebra computations... Computations finished. Integration finished. Linear algebra computations... Computations finished. Starting the integration...Starting the integration...Starting the integration...Starting the integration...Starting the integration...Starting the integration...Starting the integration... Starting the integration... Computing graph 7/50... Integration finished. Linear algebra computations... Computations finished. Integration finished. Linear algebra computations... Computations finished. Integration finished. Linear algebra computations... Computations finished. Integration finished. Linear algebra computations...Integration finished. Linear algebra computations... Computations finished. Computations finished.Integration finished. Linear algebra computations...Integration finished. Linear algebra computations... Computations finished. Computations finished. Integration finished. Linear algebra computations... Computations finished. Starting the integration...Starting the integration...Starting the integration...Starting the integration...Starting the integration...Starting the integration...Starting the integration...Starting the integration... Computing graph 8/50... Integration finished. Linear algebra computations... Computations finished. Integration finished. Linear algebra computations... Computations finished. Integration finished. Linear algebra computations... Integration finished.Computations finished. Linear algebra computations... Computations finished. Integration finished.Integration finished. Linear algebra computations...Linear algebra computations... Computations finished.Computations finished. Integration finished. Linear algebra computations... Computations finished. Integration finished. Linear algebra computations... Computations finished. Starting the integration...Starting the integration...Starting the integration...Starting the integration...Starting the integration...Starting the integration...Starting the integration... Starting the integration... Computing graph 9/50... Integration finished. Linear algebra computations... Computations finished. Integration finished. Linear algebra computations... Computations finished. Integration finished. Linear algebra computations... Computations finished. Integration finished. Linear algebra computations... Integration finished.Computations finished. Linear algebra computations... Computations finished. Integration finished. Linear algebra computations... Computations finished. Integration finished. Linear algebra computations... Computations finished. Integration finished. Linear algebra computations... Computations finished. Starting the integration...Starting the integration...Starting the integration...Starting the integration...Starting the integration...Starting the integration...Starting the integration...Starting the integration... Computing graph 10/50... Integration finished. Linear algebra computations... Computations finished. Integration finished. Linear algebra computations... Computations finished. Integration finished. Linear algebra computations... Integration finished. Computations finished.Linear algebra computations... Computations finished. Integration finished. Linear algebra computations... Computations finished. Integration finished. Linear algebra computations... Integration finished.Computations finished. Linear algebra computations... Computations finished. Integration finished. Linear algebra computations... Computations finished. Starting the integration...Starting the integration...Starting the integration...Starting the integration...Starting the integration...Starting the integration... Starting the integration...Starting the integration... Computing graph 11/50... Integration finished. Linear algebra computations... Computations finished. Integration finished. Linear algebra computations... Computations finished. Integration finished. Linear algebra computations... Integration finished.Computations finished. Linear algebra computations... Computations finished. Integration finished. Linear algebra computations... Computations finished. Integration finished. Linear algebra computations... Computations finished. Integration finished. Integration finished.Linear algebra computations... Linear algebra computations... Computations finished.Computations finished. Starting the integration...Starting the integration...Starting the integration...Starting the integration...Starting the integration...Starting the integration...Starting the integration...Starting the integration... Computing graph 12/50... Integration finished. Linear algebra computations... Computations finished. Integration finished. Linear algebra computations... Computations finished.Integration finished. Linear algebra computations... Computations finished. Integration finished. Linear algebra computations... Integration finished.Computations finished. Linear algebra computations... Computations finished. Integration finished. Linear algebra computations... Computations finished. Integration finished. Integration finished. Linear algebra computations...Linear algebra computations... Computations finished.Computations finished. Starting the integration...Starting the integration...Starting the integration...Starting the integration...Starting the integration...Starting the integration...Starting the integration... Starting the integration... Computing graph 13/50... Integration finished. Linear algebra computations... Computations finished. Integration finished. Linear algebra computations... Computations finished. Integration finished.Integration finished. Linear algebra computations...Linear algebra computations... Computations finished.Computations finished. Integration finished. Linear algebra computations... Computations finished. Integration finished. Integration finished.Linear algebra computations... Linear algebra computations... Computations finished. Computations finished. Integration finished. Linear algebra computations... Computations finished. Starting the integration...Starting the integration...Starting the integration...Starting the integration...Starting the integration...Starting the integration...Starting the integration...Starting the integration... Computing graph 14/50... Integration finished. Linear algebra computations... Computations finished. Integration finished. Linear algebra computations... Computations finished. Integration finished. Linear algebra computations... Computations finished. Integration finished. Integration finished.Linear algebra computations... Linear algebra computations... Computations finished. Computations finished. Integration finished. Linear algebra computations...Integration finished. Linear algebra computations...Computations finished. Computations finished. Integration finished. Linear algebra computations... Computations finished. Starting the integration...Starting the integration...Starting the integration...Starting the integration...Starting the integration...Starting the integration...Starting the integration...Starting the integration... Computing graph 15/50... Integration finished. Linear algebra computations... Computations finished. Integration finished. Linear algebra computations... Computations finished. Integration finished. Linear algebra computations... Computations finished. Integration finished. Linear algebra computations... Computations finished. Integration finished. Linear algebra computations... Integration finished. Computations finished.Linear algebra computations... Integration finished. Computations finished.Linear algebra computations... Computations finished. Integration finished. Linear algebra computations... Computations finished. Starting the integration...Starting the integration...Starting the integration...Starting the integration...Starting the integration...Starting the integration...Starting the integration...Starting the integration... Computing graph 16/50... Integration finished. Linear algebra computations... Computations finished. Integration finished. Linear algebra computations... Computations finished. Integration finished. Linear algebra computations... Computations finished. Integration finished. Linear algebra computations... Computations finished. Integration finished. Linear algebra computations... Integration finished.Computations finished. Integration finished.Linear algebra computations... Linear algebra computations... Computations finished.Integration finished. Computations finished.Linear algebra computations... Computations finished. Starting the integration...Starting the integration...Starting the integration...Starting the integration...Starting the integration...Starting the integration...Starting the integration... Starting the integration... Computing graph 17/50... Integration finished. Linear algebra computations... Computations finished. Integration finished. Linear algebra computations... Computations finished. Integration finished. Linear algebra computations... Computations finished. Integration finished. Linear algebra computations... Computations finished. Integration finished. Linear algebra computations... Computations finished. Integration finished. Linear algebra computations... Integration finished. Computations finished.Linear algebra computations... Computations finished. Integration finished. Linear algebra computations... Computations finished. Starting the integration...Starting the integration...Starting the integration...Starting the integration...Starting the integration...Starting the integration...Starting the integration...Starting the integration... Computing graph 18/50... Integration finished. Linear algebra computations... Computations finished. Integration finished. Linear algebra computations... Computations finished. Integration finished. Linear algebra computations... Integration finished.Computations finished. Linear algebra computations... Computations finished. Integration finished. Linear algebra computations...Integration finished. Linear algebra computations...Computations finished. Computations finished. Integration finished. Linear algebra computations... Computations finished. Integration finished. Linear algebra computations... Computations finished. Starting the integration...Starting the integration...Starting the integration...Starting the integration...Starting the integration...Starting the integration...Starting the integration... Starting the integration... Computing graph 19/50... Integration finished. Linear algebra computations... Computations finished. Integration finished. Linear algebra computations... Integration finished. Linear algebra computations...Computations finished. Computations finished. Integration finished. Linear algebra computations... Computations finished.Integration finished. Linear algebra computations... Computations finished. Integration finished. Linear algebra computations... Integration finished.Computations finished. Linear algebra computations... Computations finished. Integration finished. Linear algebra computations... Computations finished. Starting the integration...Starting the integration...Starting the integration...Starting the integration...Starting the integration...Starting the integration...Starting the integration...Starting the integration... Computing graph 20/50... Integration finished. Linear algebra computations... Computations finished. Integration finished. Linear algebra computations... Computations finished. Integration finished. Linear algebra computations... Computations finished. Integration finished. Linear algebra computations... Computations finished. Integration finished. Linear algebra computations... Computations finished. Integration finished. Linear algebra computations... Integration finished.Computations finished. Linear algebra computations... Computations finished. Integration finished. Linear algebra computations... Computations finished. Starting the integration...Starting the integration...Starting the integration...Starting the integration...Starting the integration...Starting the integration... Starting the integration...Starting the integration... Computing graph 21/50... Integration finished. Linear algebra computations... Computations finished. Integration finished. Linear algebra computations... Integration finished. Linear algebra computations...Computations finished. Integration finished.Computations finished. Linear algebra computations... Integration finished.Computations finished. Linear algebra computations... Integration finished.Computations finished. Linear algebra computations... Computations finished. Integration finished. Linear algebra computations... Computations finished. Integration finished. Linear algebra computations... Computations finished. Starting the integration...Starting the integration...Starting the integration...Starting the integration...Starting the integration... Starting the integration... Starting the integration...Starting the integration... Computing graph 22/50... Integration finished. Linear algebra computations... Computations finished. Integration finished.Integration finished. Linear algebra computations...Linear algebra computations... Computations finished.Computations finished. Integration finished. Linear algebra computations... Integration finished. Computations finished.Linear algebra computations... Computations finished. Integration finished. Linear algebra computations... Computations finished. Integration finished.Integration finished. Linear algebra computations...Linear algebra computations... Computations finished.Computations finished. Starting the integration...Starting the integration...Starting the integration...Starting the integration...Starting the integration... Starting the integration...Starting the integration...Starting the integration... Computing graph 23/50... Integration finished. Linear algebra computations... Computations finished. Integration finished. Linear algebra computations... Computations finished. Integration finished. Linear algebra computations... Computations finished. Integration finished. Linear algebra computations... Integration finished.Computations finished. Linear algebra computations... Computations finished. Integration finished. Linear algebra computations... Computations finished. Integration finished.Integration finished. Linear algebra computations...Linear algebra computations... Computations finished.Computations finished. Starting the integration...Starting the integration...Starting the integration...Starting the integration...Starting the integration... Starting the integration... Starting the integration... Starting the integration... Computing graph 24/50... Integration finished. Linear algebra computations... Computations finished. Integration finished. Linear algebra computations... Computations finished. Integration finished. Linear algebra computations... Computations finished. Integration finished. Linear algebra computations... Computations finished. Integration finished. Linear algebra computations... Integration finished. Computations finished.Linear algebra computations... Integration finished. Computations finished.Linear algebra computations... Computations finished. Integration finished. Linear algebra computations... Computations finished. Starting the integration...Starting the integration...Starting the integration...Starting the integration...Starting the integration... Starting the integration...Starting the integration... Starting the integration... Computing graph 25/50... Integration finished. Linear algebra computations... Computations finished. Integration finished. Linear algebra computations... Computations finished. Integration finished.Integration finished. Linear algebra computations...Linear algebra computations... Computations finished.Computations finished. Integration finished. Linear algebra computations... Computations finished. Integration finished. Linear algebra computations... Computations finished. Integration finished. Linear algebra computations... Computations finished. Integration finished. Linear algebra computations... Computations finished. Starting the integration...Starting the integration...Starting the integration...Starting the integration...Starting the integration...Starting the integration... Starting the integration... Starting the integration... Computing graph 26/50... Integration finished. Linear algebra computations...Integration finished. Linear algebra computations...Computations finished. Computations finished. Integration finished. Linear algebra computations... Computations finished. Integration finished. Linear algebra computations... Computations finished. Integration finished. Linear algebra computations... Computations finished. Integration finished. Linear algebra computations... Computations finished. Integration finished. Linear algebra computations... Computations finished. Integration finished. Linear algebra computations... Computations finished. Starting the integration...Starting the integration...Starting the integration...Starting the integration...Starting the integration...Starting the integration...Starting the integration...Starting the integration... Computing graph 27/50... Integration finished. Linear algebra computations... Computations finished. Integration finished. Linear algebra computations... Computations finished. Integration finished. Linear algebra computations... Computations finished. Integration finished. Linear algebra computations... Computations finished. Integration finished. Linear algebra computations... Computations finished. Integration finished. Linear algebra computations...Integration finished. Linear algebra computations...Computations finished. Computations finished. Integration finished. Linear algebra computations... Computations finished. Starting the integration...Starting the integration...Starting the integration...Starting the integration...Starting the integration...Starting the integration...Starting the integration... Starting the integration... Computing graph 28/50... Integration finished. Linear algebra computations... Computations finished. Integration finished. Linear algebra computations... Computations finished. Integration finished. Linear algebra computations... Computations finished. Integration finished. Linear algebra computations... Computations finished. Integration finished. Linear algebra computations... Computations finished. Integration finished. Linear algebra computations... Computations finished. Integration finished. Linear algebra computations... Computations finished. Integration finished. Linear algebra computations... Computations finished. Starting the integration...Starting the integration...Starting the integration...Starting the integration...Starting the integration...Starting the integration...Starting the integration...Starting the integration... Computing graph 29/50... Integration finished.Integration finished. Linear algebra computations... Linear algebra computations... Computations finished. Computations finished. Integration finished. Linear algebra computations... Computations finished. Integration finished. Linear algebra computations... Computations finished. Integration finished. Linear algebra computations... Integration finished.Computations finished. Linear algebra computations... Computations finished. Integration finished. Linear algebra computations... Computations finished. Integration finished. Linear algebra computations... Computations finished. Starting the integration...Starting the integration...Starting the integration...Starting the integration...Starting the integration...Starting the integration...Starting the integration... Starting the integration... Computing graph 30/50... Integration finished. Linear algebra computations... Computations finished. Integration finished. Linear algebra computations... Computations finished. Integration finished. Linear algebra computations... Computations finished. Integration finished. Linear algebra computations... Computations finished. Integration finished. Linear algebra computations... Computations finished. Integration finished. Linear algebra computations... Integration finished. Computations finished.Linear algebra computations... Computations finished. Integration finished. Linear algebra computations... Computations finished. Starting the integration...Starting the integration...Starting the integration...Starting the integration...Starting the integration...Starting the integration...Starting the integration... Starting the integration... Computing graph 31/50... Integration finished. Linear algebra computations... Computations finished. Integration finished. Linear algebra computations... Computations finished. Integration finished. Linear algebra computations... Computations finished. Integration finished. Linear algebra computations... Computations finished. Integration finished.Integration finished. Integration finished.Linear algebra computations...Linear algebra computations... Linear algebra computations... Integration finished.Computations finished. Computations finished.Linear algebra computations...Computations finished. Computations finished. Starting the integration...Starting the integration...Starting the integration...Starting the integration...Starting the integration...Starting the integration...Starting the integration... Starting the integration... Computing graph 32/50... Integration finished. Linear algebra computations... Computations finished. Integration finished. Linear algebra computations... Computations finished. Integration finished. Linear algebra computations... Computations finished. Integration finished. Integration finished.Linear algebra computations... Linear algebra computations... Computations finished. Computations finished. Integration finished. Linear algebra computations... Computations finished.Integration finished. Linear algebra computations... Computations finished. Integration finished. Linear algebra computations... Computations finished. Starting the integration...Starting the integration...Starting the integration...Starting the integration...Starting the integration...Starting the integration...Starting the integration...Starting the integration... Computing graph 33/50... Integration finished. Linear algebra computations... Computations finished. Integration finished. Linear algebra computations... Computations finished. Integration finished. Linear algebra computations...Integration finished. Linear algebra computations...Computations finished.Integration finished. Linear algebra computations... Computations finished. Computations finished. Integration finished. Linear algebra computations... Computations finished. Integration finished. Linear algebra computations... Computations finished.Integration finished. Linear algebra computations... Computations finished. Starting the integration...Starting the integration...Starting the integration...Starting the integration...Starting the integration...Starting the integration...Starting the integration... Starting the integration... Computing graph 34/50... Integration finished. Linear algebra computations... Computations finished. Integration finished. Linear algebra computations... Computations finished. Integration finished. Linear algebra computations... Computations finished. Integration finished. Linear algebra computations... Computations finished. Integration finished. Linear algebra computations...Integration finished.Integration finished. Computations finished.Linear algebra computations...Linear algebra computations... Computations finished.Computations finished. Integration finished. Linear algebra computations... Computations finished. Starting the integration...Starting the integration...Starting the integration...Starting the integration...Starting the integration...Starting the integration...Starting the integration...Starting the integration... Computing graph 35/50... Integration finished. Linear algebra computations... Computations finished. Integration finished. Linear algebra computations... Computations finished. Integration finished. Linear algebra computations... Computations finished. Integration finished. Linear algebra computations... Computations finished. Integration finished.Integration finished. Linear algebra computations...Linear algebra computations... Computations finished.Computations finished. Integration finished. Linear algebra computations... Computations finished. Integration finished. Linear algebra computations... Computations finished. Starting the integration...Starting the integration...Starting the integration...Starting the integration...Starting the integration...Starting the integration...Starting the integration... Starting the integration... Computing graph 36/50... Integration finished. Linear algebra computations... Computations finished. Integration finished. Linear algebra computations... Computations finished. Integration finished. Linear algebra computations... Computations finished. Integration finished. Linear algebra computations... Computations finished. Integration finished. Linear algebra computations... Computations finished. Integration finished. Linear algebra computations... Computations finished. Integration finished. Linear algebra computations... Computations finished. Integration finished. Linear algebra computations... Computations finished. Starting the integration...Starting the integration... Starting the integration...Starting the integration...Starting the integration...Starting the integration...Starting the integration... Starting the integration... Computing graph 37/50... Integration finished. Linear algebra computations... Computations finished. Integration finished. Linear algebra computations... Computations finished. Integration finished. Linear algebra computations... Computations finished. Integration finished. Linear algebra computations... Computations finished.Integration finished. Linear algebra computations... Computations finished. Integration finished. Linear algebra computations... Computations finished. Integration finished. Linear algebra computations... Computations finished. Integration finished. Linear algebra computations... Computations finished. Starting the integration...Starting the integration...Starting the integration...Starting the integration...Starting the integration...Starting the integration...Starting the integration...Starting the integration... Computing graph 38/50... Integration finished. Linear algebra computations... Computations finished. Integration finished. Linear algebra computations... Computations finished. Integration finished. Linear algebra computations... Computations finished. Integration finished. Linear algebra computations... Computations finished. Integration finished. Linear algebra computations... Computations finished. Integration finished. Linear algebra computations... Computations finished. Integration finished. Linear algebra computations... Computations finished. Integration finished. Linear algebra computations... Computations finished. Starting the integration...Starting the integration...Starting the integration...Starting the integration...Starting the integration...Starting the integration...Starting the integration... Starting the integration... Computing graph 39/50... Integration finished. Linear algebra computations... Computations finished. Integration finished. Linear algebra computations... Computations finished. Integration finished. Linear algebra computations... Computations finished. Integration finished. Linear algebra computations... Computations finished. Integration finished. Linear algebra computations... Computations finished. Integration finished. Linear algebra computations... Integration finished.Computations finished. Linear algebra computations... Integration finished. Computations finished.Linear algebra computations... Computations finished. Starting the integration...Starting the integration...Starting the integration...Starting the integration...Starting the integration...Starting the integration...Starting the integration... Starting the integration... Computing graph 40/50... Integration finished. Linear algebra computations... Computations finished. Integration finished. Linear algebra computations... Computations finished. Integration finished. Integration finished.Linear algebra computations... Linear algebra computations... Computations finished. Computations finished. Integration finished. Linear algebra computations... Computations finished. Integration finished. Linear algebra computations... Computations finished. Integration finished. Linear algebra computations...Integration finished. Linear algebra computations...Computations finished. Computations finished. Starting the integration...Starting the integration...Starting the integration...Starting the integration...Starting the integration...Starting the integration...Starting the integration...Starting the integration... Computing graph 41/50... Integration finished. Linear algebra computations... Computations finished. Integration finished. Linear algebra computations... Computations finished. Integration finished. Linear algebra computations... Computations finished. Integration finished. Linear algebra computations... Integration finished. Computations finished.Linear algebra computations... Computations finished. Integration finished. Linear algebra computations... Computations finished. Integration finished. Linear algebra computations... Integration finished. Linear algebra computations...Computations finished. Computations finished. Starting the integration...Starting the integration...Starting the integration...Starting the integration...Starting the integration... Starting the integration...Starting the integration...Starting the integration... Computing graph 42/50... Integration finished. Linear algebra computations... Computations finished. Integration finished. Linear algebra computations... Computations finished. Integration finished. Linear algebra computations... Computations finished. Integration finished. Linear algebra computations... Computations finished. Integration finished. Linear algebra computations... Computations finished. Integration finished. Linear algebra computations... Integration finished. Computations finished.Linear algebra computations... Computations finished. Integration finished. Linear algebra computations... The critical eigenvalue is not in the range of the dispersion relation. The linear analysis cannot be performed. The critical eigenvalue is: -2.185771349294377
/tmp/ipykernel_1027/3001995589.py:147: RuntimeWarning: invalid value encountered in scalar divide ipr_eigenvector = np.sum(critical_eigenvector**4) / (np.sum(critical_eigenvector**2)**2)
Computations finished. Starting the integration...Starting the integration...Starting the integration...Starting the integration...Starting the integration...Starting the integration...Starting the integration...Starting the integration... Computing graph 43/50... Integration finished. Linear algebra computations... Computations finished. Integration finished. Linear algebra computations... Computations finished. Integration finished. Linear algebra computations... Computations finished. Integration finished. Linear algebra computations... The critical eigenvalue is not in the range of the dispersion relation. The linear analysis cannot be performed. The critical eigenvalue is: -2.5381982318695693
/tmp/ipykernel_1027/3001995589.py:147: RuntimeWarning: invalid value encountered in scalar divide ipr_eigenvector = np.sum(critical_eigenvector**4) / (np.sum(critical_eigenvector**2)**2)
Computations finished. Integration finished. Linear algebra computations... Computations finished. Integration finished. Linear algebra computations... Computations finished. Integration finished. Linear algebra computations... Computations finished. Integration finished. Linear algebra computations... Computations finished. Starting the integration...Starting the integration...Starting the integration...Starting the integration...Starting the integration...Starting the integration...Starting the integration...Starting the integration... Computing graph 44/50... Integration finished. Linear algebra computations... Computations finished. Integration finished. Linear algebra computations... Computations finished. Integration finished. Linear algebra computations... The critical eigenvalue is not in the range of the dispersion relation. The linear analysis cannot be performed. The critical eigenvalue is: 8.881784197001252e-16
/tmp/ipykernel_1027/3001995589.py:147: RuntimeWarning: invalid value encountered in scalar divide ipr_eigenvector = np.sum(critical_eigenvector**4) / (np.sum(critical_eigenvector**2)**2)
Computations finished. Integration finished. Linear algebra computations... The critical eigenvalue is not in the range of the dispersion relation. Integration finished.The linear analysis cannot be performed. Linear algebra computations...The critical eigenvalue is: -2.4207140732126824The critical eigenvalue is not in the range of the dispersion relation.
/tmp/ipykernel_1027/3001995589.py:147: RuntimeWarning: invalid value encountered in scalar divide ipr_eigenvector = np.sum(critical_eigenvector**4) / (np.sum(critical_eigenvector**2)**2)
The linear analysis cannot be performed.Computations finished. The critical eigenvalue is: -2.589536457801767 Computations finished. Integration finished.Integration finished. Linear algebra computations...Linear algebra computations... Computations finished.Computations finished.Integration finished. Linear algebra computations... Computations finished. Starting the integration...Starting the integration...Starting the integration...Starting the integration...Starting the integration...Starting the integration...Starting the integration... Starting the integration... Computing graph 45/50... Integration finished. Linear algebra computations... The critical eigenvalue is not in the range of the dispersion relation. The linear analysis cannot be performed. Integration finished.The critical eigenvalue is: Linear algebra computations...-2.5124816146229656
/tmp/ipykernel_1027/3001995589.py:147: RuntimeWarning: invalid value encountered in scalar divide ipr_eigenvector = np.sum(critical_eigenvector**4) / (np.sum(critical_eigenvector**2)**2)
Computations finished. The critical eigenvalue is not in the range of the dispersion relation. The linear analysis cannot be performed. The critical eigenvalue is: -2.281055244917911
/tmp/ipykernel_1027/3001995589.py:147: RuntimeWarning: invalid value encountered in scalar divide ipr_eigenvector = np.sum(critical_eigenvector**4) / (np.sum(critical_eigenvector**2)**2)
Computations finished. Integration finished. Linear algebra computations... The critical eigenvalue is not in the range of the dispersion relation.Integration finished. The linear analysis cannot be performed. Linear algebra computations...The critical eigenvalue is: -2.4578211740250353The critical eigenvalue is not in the range of the dispersion relation. Computations finished.The linear analysis cannot be performed. The critical eigenvalue is: -2.5739038435598554
/tmp/ipykernel_1027/3001995589.py:147: RuntimeWarning: invalid value encountered in scalar divide ipr_eigenvector = np.sum(critical_eigenvector**4) / (np.sum(critical_eigenvector**2)**2)
Computations finished. Integration finished. Linear algebra computations... The critical eigenvalue is not in the range of the dispersion relation. The linear analysis cannot be performed. Integration finished.The critical eigenvalue is: Linear algebra computations...-8.881784197001252e-16 The critical eigenvalue is not in the range of the dispersion relation.
/tmp/ipykernel_1027/3001995589.py:147: RuntimeWarning: invalid value encountered in scalar divide ipr_eigenvector = np.sum(critical_eigenvector**4) / (np.sum(critical_eigenvector**2)**2)
Computations finished.The linear analysis cannot be performed.Integration finished. The critical eigenvalue is: Linear algebra computations... -2.462970217952612 The critical eigenvalue is not in the range of the dispersion relation.
/tmp/ipykernel_1027/3001995589.py:147: RuntimeWarning: invalid value encountered in scalar divide ipr_eigenvector = np.sum(critical_eigenvector**4) / (np.sum(critical_eigenvector**2)**2)
Computations finished.The linear analysis cannot be performed. The critical eigenvalue is: 8.881784197001252e-16
/tmp/ipykernel_1027/3001995589.py:147: RuntimeWarning: invalid value encountered in scalar divide ipr_eigenvector = np.sum(critical_eigenvector**4) / (np.sum(critical_eigenvector**2)**2)
Computations finished. Integration finished. Linear algebra computations... The critical eigenvalue is not in the range of the dispersion relation. The linear analysis cannot be performed. The critical eigenvalue is: 1.3322676295501878e-15 Computations finished. Starting the integration...Starting the integration...Starting the integration...Starting the integration...Starting the integration...Starting the integration...Starting the integration... Starting the integration... Computing graph 46/50... Integration finished. Linear algebra computations... The critical eigenvalue is not in the range of the dispersion relation. The linear analysis cannot be performed. The critical eigenvalue is: Integration finished.1.7763568394002505e-15 Linear algebra computations...Computations finished. The critical eigenvalue is not in the range of the dispersion relation. The linear analysis cannot be performed. The critical eigenvalue is: Integration finished. 8.881784197001252e-16Linear algebra computations... Computations finished. The critical eigenvalue is not in the range of the dispersion relation. The linear analysis cannot be performed.Integration finished. The critical eigenvalue is: Linear algebra computations... -8.881784197001252e-16 The critical eigenvalue is not in the range of the dispersion relation.
/tmp/ipykernel_1027/3001995589.py:147: RuntimeWarning: invalid value encountered in scalar divide ipr_eigenvector = np.sum(critical_eigenvector**4) / (np.sum(critical_eigenvector**2)**2)
The linear analysis cannot be performed.Computations finished. The critical eigenvalue is: 0.0
/tmp/ipykernel_1027/3001995589.py:147: RuntimeWarning: invalid value encountered in scalar divide ipr_eigenvector = np.sum(critical_eigenvector**4) / (np.sum(critical_eigenvector**2)**2)
Computations finished. Integration finished. Linear algebra computations... The critical eigenvalue is not in the range of the dispersion relation. The linear analysis cannot be performed. The critical eigenvalue is: -1.7763568394002505e-15 Computations finished. Integration finished. Linear algebra computations... The critical eigenvalue is not in the range of the dispersion relation. The linear analysis cannot be performed. The critical eigenvalue is: 1.047129243061654e-15 Computations finished. Integration finished. Linear algebra computations... The critical eigenvalue is not in the range of the dispersion relation. The linear analysis cannot be performed. The critical eigenvalue is: 4.440892098500626e-16 Computations finished. Integration finished. Linear algebra computations... The critical eigenvalue is not in the range of the dispersion relation. The linear analysis cannot be performed. The critical eigenvalue is: -2.6645352591003757e-15 Computations finished. Starting the integration...Starting the integration...Starting the integration...Starting the integration...Starting the integration...Starting the integration...Starting the integration... Starting the integration... Computing graph 47/50... Integration finished. Linear algebra computations... The critical eigenvalue is not in the range of the dispersion relation. The linear analysis cannot be performed. The critical eigenvalue is: 4.440892098500626e-16 Computations finished. Integration finished. Linear algebra computations... The critical eigenvalue is not in the range of the dispersion relation. The linear analysis cannot be performed. The critical eigenvalue is: -1.7763568394002505e-15 Computations finished. Integration finished. Linear algebra computations... The critical eigenvalue is not in the range of the dispersion relation. The linear analysis cannot be performed. The critical eigenvalue is: 8.881784197001252e-16 Computations finished. Integration finished. Integration finished.Linear algebra computations... Linear algebra computations... The critical eigenvalue is not in the range of the dispersion relation. The critical eigenvalue is not in the range of the dispersion relation.The linear analysis cannot be performed. The linear analysis cannot be performed.The critical eigenvalue is: The critical eigenvalue is: -1.3322676295501878e-15 -8.881784197001252e-16Computations finished. Computations finished. Integration finished. Linear algebra computations... The critical eigenvalue is not in the range of the dispersion relation. The linear analysis cannot be performed. The critical eigenvalue is: 8.881784197001252e-16 Computations finished. Integration finished. Integration finished.Linear algebra computations... Linear algebra computations... The critical eigenvalue is not in the range of the dispersion relation. The linear analysis cannot be performed. The critical eigenvalue is not in the range of the dispersion relation.The critical eigenvalue is: The linear analysis cannot be performed.0.0 The critical eigenvalue is: Computations finished. -8.881784197001252e-16 Computations finished. Starting the integration...Starting the integration...Starting the integration...Starting the integration...Starting the integration...Starting the integration... Starting the integration...Starting the integration... Computing graph 48/50... Integration finished. Linear algebra computations... The critical eigenvalue is not in the range of the dispersion relation. The linear analysis cannot be performed. The critical eigenvalue is: 4.041714481980183e-15 Computations finished. Integration finished. Linear algebra computations...Integration finished. Linear algebra computations...The critical eigenvalue is not in the range of the dispersion relation. The linear analysis cannot be performed.The critical eigenvalue is not in the range of the dispersion relation. The critical eigenvalue is: The linear analysis cannot be performed. 0.0 The critical eigenvalue is: Computations finished. 8.881784197001252e-16 Computations finished. Integration finished. Linear algebra computations... The critical eigenvalue is not in the range of the dispersion relation. The linear analysis cannot be performed. The critical eigenvalue is: 8.881784197001252e-16 Computations finished. Integration finished. Linear algebra computations... The critical eigenvalue is not in the range of the dispersion relation. The linear analysis cannot be performed. The critical eigenvalue is: 0.0 Computations finished. Integration finished. Linear algebra computations... The critical eigenvalue is not in the range of the dispersion relation. The linear analysis cannot be performed. The critical eigenvalue is: -3.552713678800501e-15 Computations finished. Integration finished. Linear algebra computations... The critical eigenvalue is not in the range of the dispersion relation. The linear analysis cannot be performed. The critical eigenvalue is: -2.220446049250313e-15 Computations finished. Integration finished. Linear algebra computations... The critical eigenvalue is not in the range of the dispersion relation. The linear analysis cannot be performed. The critical eigenvalue is: 2.509817662595573e-16 Computations finished. Starting the integration...Starting the integration...Starting the integration...Starting the integration...Starting the integration...Starting the integration... Starting the integration...Starting the integration... Computing graph 49/50... Integration finished. Linear algebra computations... The critical eigenvalue is not in the range of the dispersion relation. The linear analysis cannot be performed. The critical eigenvalue is: 4.915748542778049e-16 Computations finished. Integration finished. Linear algebra computations... The critical eigenvalue is not in the range of the dispersion relation. The linear analysis cannot be performed. The critical eigenvalue is: 0.0 Computations finished. Integration finished.Integration finished. Linear algebra computations...Linear algebra computations... The critical eigenvalue is not in the range of the dispersion relation.The critical eigenvalue is not in the range of the dispersion relation. The linear analysis cannot be performed.The linear analysis cannot be performed. The critical eigenvalue is: The critical eigenvalue is: 3.552713678800501e-151.7763568394002505e-15 Computations finished.Computations finished. Integration finished. Integration finished.Linear algebra computations... Linear algebra computations... The critical eigenvalue is not in the range of the dispersion relation. The critical eigenvalue is not in the range of the dispersion relation.The linear analysis cannot be performed. The linear analysis cannot be performed.The critical eigenvalue is: The critical eigenvalue is: -1.2690089419017577e-15 3.552713678800501e-15Computations finished. Computations finished. Integration finished. Linear algebra computations... Integration finished. The critical eigenvalue is not in the range of the dispersion relation.Linear algebra computations... The linear analysis cannot be performed. The critical eigenvalue is not in the range of the dispersion relation.The critical eigenvalue is: The linear analysis cannot be performed.-1.7763568394002505e-15 The critical eigenvalue is: Computations finished. -2.6645352591003757e-15 Computations finished. Starting the integration...Starting the integration...Starting the integration...Starting the integration... Starting the integration...Starting the integration... Starting the integration...Starting the integration... Computing graph 50/50... Integration finished. Linear algebra computations... The critical eigenvalue is not in the range of the dispersion relation. The linear analysis cannot be performed. The critical eigenvalue is: -8.881784197001252e-16 Computations finished. Integration finished. Linear algebra computations... The critical eigenvalue is not in the range of the dispersion relation. The linear analysis cannot be performed. The critical eigenvalue is: 0.0 Computations finished. Integration finished. Linear algebra computations... The critical eigenvalue is not in the range of the dispersion relation. The linear analysis cannot be performed. The critical eigenvalue is: 1.7763568394002505e-15 Computations finished. Integration finished. Linear algebra computations... The critical eigenvalue is not in the range of the dispersion relation. The linear analysis cannot be performed.Integration finished. Linear algebra computations... The critical eigenvalue is not in the range of the dispersion relation. The linear analysis cannot be performed.The critical eigenvalue is: The critical eigenvalue is: -8.881784197001252e-16 -2.8222448992052524e-15Computations finished. Integration finished.Computations finished. Linear algebra computations... The critical eigenvalue is not in the range of the dispersion relation. The linear analysis cannot be performed. The critical eigenvalue is: 0.0 Computations finished. Integration finished.Integration finished. Linear algebra computations...Linear algebra computations... The critical eigenvalue is not in the range of the dispersion relation.The critical eigenvalue is not in the range of the dispersion relation. The linear analysis cannot be performed.The linear analysis cannot be performed. The critical eigenvalue is: The critical eigenvalue is: 0.0-9.292183877208547e-16 Computations finished.Computations finished. Plotting the results...
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0.0021091929097053755, 0.002054641838041386, 0.0038433357843689186, 0.0025241187634264454, 0.005686489687650889, 0.0057676552301816515], [0.006186173106367765, 0.002665177119875556, 0.006140963241358957, 0.0012297422146925758, 0.0006201089244050523, 0.001115945661972791, 0.001354081561595481, 0.0064808507666410655], [0.001962923747116546, 0.0003476598280540634, 0.0018625709018290787, 0.0018802223685780953, 0.001201322784587703, 0.004771121042177683, 0.00013830672106239503, 0.0018945729355494012], [0.00026004885548017897, 0.00016349323605417142, 0.0007157775863904168, 0.0004602578445117602, 0.0016397040910818353, 0.0047625349136402725, 0.0009840683551743056, 7.00081397353968e-05], [2.5714311139919186e-05, 0.00024839922788478646, 0.0006618188892321214, 0.00014487403889209158, 0.00019344511324383243, 0.00512312563205296, 0.005029627788353295, 0.0020187030774238405], [0.00012798806143312242, 3.634425923376752e-05, 6.690255082914062e-05, 0.0001831708193529316, 0.00022474449701211205, 0.0001989805601727384, 4.8034558541334245e-05, 3.230810111451904e-05], [2.7069220555595347e-06, 8.107184578281131e-05, 2.158583752464265e-06, 1.9299835228472796e-05, 4.601818428502058e-06, 7.626455960154196e-05, 4.249524159463922e-06, 0.0001225735540513529]], 'data_variance_eigenvector': [[0.04000000000000001, 0.04000000000000001, 0.04000000000000001, 0.04000000000000001, 0.04000000000000001, 0.04000000000000001, 0.04000000000000001, 0.04000000000000001], [0.04000000000000001, 0.04000000000000001, 0.04000000000000001, 0.04000000000000001, 0.04000000000000001, 0.04000000000000001, 0.04000000000000001, 0.04000000000000001], [0.04000000000000001, 0.04000000000000001, 0.04000000000000001, 0.04000000000000001, 0.04000000000000001, 0.04000000000000001, 0.04000000000000001, 0.04000000000000001], [0.04000000000000001, 0.04000000000000001, 0.04000000000000001, 0.04000000000000001, 0.04000000000000001, 0.04000000000000001, 0.04000000000000001, 0.04000000000000001], [0.04000000000000001, 0.04000000000000001, 0.04000000000000001, 0.04000000000000001, 0.04000000000000001, 0.04000000000000001, 0.04000000000000001, 0.04000000000000001], [0.04000000000000001, 0.04000000000000001, 0.04000000000000001, 0.04000000000000001, 0.04000000000000001, 0.04000000000000001, 0.04000000000000001, 0.04000000000000001], [0.04000000000000001, 0.04000000000000001, 0.04000000000000001, 0.04000000000000001, 0.04000000000000001, 0.04000000000000001, 0.04000000000000001, 0.04000000000000001], [0.04000000000000001, 0.04000000000000001, 0.04000000000000001, 0.04000000000000001, 0.04000000000000001, 0.04000000000000001, 0.04000000000000001, 0.04000000000000001], [0.04000000000000001, 0.04000000000000001, 0.04000000000000001, 0.04000000000000001, 0.04000000000000001, 0.04000000000000001, 0.04000000000000001, 0.04000000000000001], [0.04000000000000001, 0.04000000000000001, 0.04000000000000001, 0.04000000000000001, 0.04000000000000001, 0.04000000000000001, 0.04000000000000001, 0.04000000000000001], [0.04000000000000001, 0.04000000000000001, 0.04000000000000001, 0.04000000000000001, 0.04000000000000001, 0.04000000000000001, 0.04000000000000001, 0.04000000000000001], [0.04000000000000001, 0.04000000000000001, 0.04000000000000001, 0.04000000000000001, 0.04000000000000001, 0.04000000000000001, 0.04000000000000001, 0.04000000000000001], [0.04000000000000001, 0.04000000000000001, 0.04000000000000001, 0.04000000000000001, 0.04000000000000001, 0.04000000000000001, 0.04000000000000001, 0.04000000000000001], [0.04000000000000001, 0.04000000000000001, 0.04000000000000001, 0.04000000000000001, 0.04000000000000001, 0.04000000000000001, 0.04000000000000001, 0.04000000000000001], [0.04000000000000001, 0.04000000000000001, 0.04000000000000001, 0.04000000000000001, 0.04000000000000001, 0.04000000000000001, 0.04000000000000001, 0.04000000000000001], [0.04000000000000001, 0.04000000000000001, 0.04000000000000001, 0.04000000000000001, 0.04000000000000001, 0.04000000000000001, 0.04000000000000001, 0.04000000000000001], [0.04000000000000001, 0.04000000000000001, 0.04000000000000001, 0.04000000000000001, 0.04000000000000001, 0.039999999999999994, 0.04000000000000001, 0.04000000000000001], [0.04000000000000001, 0.04000000000000001, 0.04000000000000001, 0.04000000000000001, 0.04000000000000001, 0.039999999999999994, 0.04000000000000001, 0.04000000000000001], [0.04000000000000001, 0.04000000000000001, 0.04000000000000001, 0.04000000000000001, 0.04000000000000001, 0.039999999999999994, 0.04000000000000001, 0.04000000000000001], [0.04000000000000001, 0.04000000000000001, 0.04000000000000001, 0.04000000000000001, 0.04000000000000001, 0.039999999999999994, 0.04000000000000001, 0.04000000000000001], [0.04000000000000001, 0.04000000000000001, 0.04000000000000001, 0.04000000000000001, 0.04000000000000001, 0.039999999999999994, 0.04000000000000001, 0.04000000000000001], [0.04000000000000001, 0.04000000000000001, 0.04000000000000001, 0.04000000000000001, 0.04000000000000001, 0.039999999999999994, 0.04000000000000001, 0.04000000000000001], [0.04000000000000001, 0.04000000000000001, 0.04000000000000001, 0.04000000000000001, 0.04000000000000001, 0.039999999999999994, 0.04000000000000001, 0.04000000000000001], [0.04000000000000001, 0.04000000000000001, 0.04000000000000001, 0.04000000000000001, 0.04000000000000001, 0.039999999999999994, 0.04000000000000001, 0.04000000000000001], [0.04000000000000001, 0.04000000000000001, 0.04000000000000001, 0.04000000000000001, 0.04000000000000001, 0.039999999999999994, 0.04000000000000001, 0.04000000000000001], [0.04000000000000001, 0.04, 0.04000000000000001, 0.04000000000000001, 0.04000000000000001, 0.039999999999999994, 0.04000000000000001, 0.04000000000000001], [0.04000000000000001, 0.04, 0.04000000000000001, 0.04, 0.04000000000000001, 0.04000000000000001, 0.04000000000000001, 0.04000000000000001], [0.039999999999999994, 0.04, 0.04000000000000001, 0.04, 0.04000000000000001, 0.04000000000000001, 0.04000000000000001, 0.04000000000000001], [0.039999999999999994, 0.04, 0.04000000000000001, 0.04, 0.04000000000000001, 0.04000000000000001, 0.04000000000000001, 0.04000000000000001], [0.039999999999999994, 0.04000000000000001, 0.04000000000000001, 0.04, 0.04000000000000001, 0.04000000000000001, 0.04, 0.04000000000000001], [0.039999999999999994, 0.04000000000000001, 0.039999999999999994, 0.04, 0.04000000000000001, 0.04000000000000001, 0.04, 0.04000000000000001], [0.039999999999999994, 0.04, 0.039999999999999994, 0.039999999999999994, 0.04000000000000001, 0.04, 0.039999999999999994, 0.04000000000000001], [0.039999999999999994, 0.04, 0.04, 0.04, 0.04000000000000001, 0.04, 0.039999999999999994, 0.04000000000000001], [0.039999999999999994, 0.04, 0.04, 0.04, 0.039999999999999994, 0.04, 0.039999999999999994, 0.04000000000000001], [0.039999999999999994, 0.04, 0.04000000000000001, 0.04, 0.039999999999999994, 0.04, 0.039999999999999994, 0.04], [0.039999999999999994, 0.04, 0.04000000000000001, 0.04000000000000001, 0.04000000000000001, 0.039999999999999994, 0.039999999999999994, 0.039999999999999994], [0.039999999999999994, 0.039999999999999994, 0.04000000000000001, 0.04000000000000001, 0.04000000000000001, 0.039999999999999994, 0.039999999999999994, 0.04], [0.04000000000000001, 0.04, 0.04000000000000001, 0.04000000000000001, 0.04000000000000001, 0.039999999999999994, 0.039999999999999994, 0.04], [0.04000000000000001, 0.04, 0.04000000000000001, 0.039999999999999994, 0.039999999999999994, 0.04000000000000001, 0.039999999999999994, 0.039999999999999994], [0.04000000000000001, 0.039999999999999994, 0.04000000000000001, 0.04, 0.04000000000000001, 0.039999999999999994, 0.039999999999999994, 0.039999999999999994], [0.04000000000000001, 0.040000000000000015, 0.039999999999999994, 0.04000000000000001, 0.039999999999999994, 0.04000000000000001, 0.039999999999999994, 0.039999999999999994], [0.04000000000000001, 0.04, 0.039999999999999994, 0.039999999999999994, 0.0, 0.039999999999999994, 0.04, 0.04000000000000001], [0.04, 0.039999999999999994, 0.04, 0.039999999999999994, 0.0, 0.04, 0.04, 0.04000000000000001], [0.04000000000000001, 0.04, 0.03999999999999999, 0.0, 0.0, 0.0, 0.04, 0.04000000000000001], [0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0], [0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0], [0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0], [0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0], [0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0], [0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0]], 'data_k_avg': [[6.0, 6.0, 6.0, 6.0, 6.0, 6.0, 6.0, 6.0], [6.0, 6.0, 6.0, 6.0, 6.0, 6.0, 6.0, 6.0], [6.0, 6.0, 6.0, 6.0, 6.0, 6.0, 6.0, 6.0], [6.0, 6.0, 6.0, 6.0, 6.0, 6.0, 6.0, 6.0], [6.0, 6.0, 6.0, 6.0, 6.0, 6.0, 6.0, 6.0], [6.0, 6.0, 6.0, 6.0, 6.0, 6.0, 6.0, 6.0], [6.0, 6.0, 6.0, 6.0, 6.0, 6.0, 6.0, 6.0], [6.0, 6.0, 6.0, 6.0, 6.0, 6.0, 6.0, 6.0], [6.0, 6.0, 6.0, 6.0, 6.0, 6.0, 6.0, 6.0], [6.0, 6.0, 6.0, 6.0, 6.0, 6.0, 6.08, 6.0], [6.0, 6.0, 6.0, 6.0, 6.0, 6.0, 6.08, 6.0], [6.0, 6.0, 6.0, 6.0, 6.0, 6.0, 6.08, 6.0], [6.0, 6.0, 6.0, 6.0, 6.0, 6.0, 6.08, 6.0], [6.08, 6.0, 6.0, 6.0, 6.0, 6.0, 6.08, 6.0], [6.08, 6.0, 6.0, 6.0, 6.0, 6.0, 6.08, 6.0], [6.08, 6.0, 6.0, 6.0, 6.0, 6.0, 6.08, 6.0], [6.08, 6.0, 6.0, 6.0, 6.0, 6.08, 6.08, 6.0], [6.08, 6.08, 6.0, 6.0, 6.0, 6.08, 6.08, 6.0], [6.08, 6.08, 6.0, 6.0, 6.0, 6.08, 6.08, 6.0], [6.08, 6.08, 6.0, 6.0, 6.0, 6.16, 6.08, 6.0], [6.08, 6.08, 6.0, 6.0, 6.0, 6.16, 6.08, 6.0], [6.08, 6.08, 6.0, 6.0, 6.0, 6.16, 6.08, 6.0], [6.08, 6.08, 6.0, 6.0, 6.0, 6.16, 6.08, 6.0], [6.08, 6.08, 6.0, 6.0, 6.0, 6.16, 6.08, 6.0], [6.08, 6.08, 6.0, 6.0, 6.0, 6.16, 6.08, 6.0], [6.08, 6.16, 6.0, 6.0, 6.0, 6.16, 6.08, 6.0], [6.08, 6.16, 6.0, 6.08, 6.0, 6.24, 6.08, 6.0], [6.08, 6.16, 6.0, 6.08, 6.0, 6.24, 6.08, 6.0], [6.08, 6.16, 6.0, 6.08, 6.0, 6.24, 6.08, 6.0], [6.08, 6.24, 6.0, 6.08, 6.0, 6.24, 6.24, 6.0], [6.08, 6.24, 6.08, 6.08, 6.0, 6.24, 6.24, 6.0], [6.16, 6.4, 6.08, 6.24, 6.0, 6.24, 6.32, 6.0], [6.16, 6.4, 6.08, 6.24, 6.0, 6.24, 6.32, 6.08], [6.16, 6.4, 6.08, 6.32, 6.16, 6.24, 6.32, 6.08], [6.16, 6.4, 6.16, 6.32, 6.16, 6.4, 6.32, 6.24], [6.24, 6.4, 6.16, 6.88, 6.4, 6.56, 6.32, 6.48], [6.24, 6.64, 6.16, 6.88, 6.56, 6.56, 6.32, 6.8], [6.8, 6.88, 6.16, 6.88, 6.64, 6.56, 6.64, 7.12], [6.72, 6.88, 6.16, 7.04, 6.88, 7.04, 6.72, 7.28], [6.8, 6.88, 6.16, 7.28, 6.96, 7.12, 6.72, 7.28], [6.8, 6.88, 6.48, 7.36, 6.96, 7.2, 6.96, 7.28], [6.88, 7.12, 6.48, 7.52, 7.44, 7.6, 7.2, 7.44], [7.52, 7.28, 6.64, 7.84, 7.6, 7.76, 7.44, 7.52], [7.44, 7.36, 6.88, 8.24, 8.16, 8.16, 7.68, 8.08], [8.08, 7.84, 7.68, 8.4, 8.8, 8.8, 8.48, 8.4], [8.64, 8.48, 8.32, 8.88, 9.04, 9.36, 8.96, 9.44], [9.12, 9.52, 8.8, 9.6, 9.44, 9.36, 9.6, 10.16], [9.84, 9.92, 10.08, 10.24, 10.08, 10.32, 10.0, 10.64], [10.48, 11.04, 10.8, 10.64, 11.2, 11.12, 11.12, 11.2], [12.0, 12.0, 12.0, 12.0, 12.0, 12.0, 12.0, 12.0]]}
In [25]:
experiment_3 = experiments(40, 8, 50, 8, params)
print(experiment_3)
Starting the experiments... Starting the integration...Starting the integration...Starting the integration...Starting the integration... Starting the integration...Starting the integration...Starting the integration... Starting the integration... Computing graph 1/50... Integration finished. Linear algebra computations... Computations finished.
/tmp/ipykernel_1027/3001995589.py:160: ComplexWarning: Casting complex values to real discards the imaginary part 'critical_eigenvalue': float(eigenvalues[index_lambda_c]), /tmp/ipykernel_1027/3001995589.py:170: ComplexWarning: Casting complex values to real discards the imaginary part 'ipr_eigenvector': float(ipr_eigenvector),
Integration finished. Linear algebra computations... Computations finished.
/tmp/ipykernel_1027/3001995589.py:160: ComplexWarning: Casting complex values to real discards the imaginary part 'critical_eigenvalue': float(eigenvalues[index_lambda_c]), /tmp/ipykernel_1027/3001995589.py:170: ComplexWarning: Casting complex values to real discards the imaginary part 'ipr_eigenvector': float(ipr_eigenvector),
Integration finished. Linear algebra computations... Computations finished.
/tmp/ipykernel_1027/3001995589.py:160: ComplexWarning: Casting complex values to real discards the imaginary part 'critical_eigenvalue': float(eigenvalues[index_lambda_c]), /tmp/ipykernel_1027/3001995589.py:170: ComplexWarning: Casting complex values to real discards the imaginary part 'ipr_eigenvector': float(ipr_eigenvector),
Integration finished. Integration finished.Linear algebra computations... Linear algebra computations...Integration finished. Linear algebra computations...Computations finished. Computations finished.
/tmp/ipykernel_1027/3001995589.py:160: ComplexWarning: Casting complex values to real discards the imaginary part 'critical_eigenvalue': float(eigenvalues[index_lambda_c]),
/tmp/ipykernel_1027/3001995589.py:170: ComplexWarning: Casting complex values to real discards the imaginary part 'ipr_eigenvector': float(ipr_eigenvector), /tmp/ipykernel_1027/3001995589.py:160: ComplexWarning: Casting complex values to real discards the imaginary part 'critical_eigenvalue': float(eigenvalues[index_lambda_c]),
Computations finished.
/tmp/ipykernel_1027/3001995589.py:170: ComplexWarning: Casting complex values to real discards the imaginary part 'ipr_eigenvector': float(ipr_eigenvector),
/tmp/ipykernel_1027/3001995589.py:160: ComplexWarning: Casting complex values to real discards the imaginary part 'critical_eigenvalue': float(eigenvalues[index_lambda_c]), /tmp/ipykernel_1027/3001995589.py:170: ComplexWarning: Casting complex values to real discards the imaginary part 'ipr_eigenvector': float(ipr_eigenvector),
Integration finished. Linear algebra computations... Computations finished.
/tmp/ipykernel_1027/3001995589.py:160: ComplexWarning: Casting complex values to real discards the imaginary part 'critical_eigenvalue': float(eigenvalues[index_lambda_c]), /tmp/ipykernel_1027/3001995589.py:170: ComplexWarning: Casting complex values to real discards the imaginary part 'ipr_eigenvector': float(ipr_eigenvector),
Integration finished. Linear algebra computations... Computations finished.
/tmp/ipykernel_1027/3001995589.py:160: ComplexWarning: Casting complex values to real discards the imaginary part 'critical_eigenvalue': float(eigenvalues[index_lambda_c]), /tmp/ipykernel_1027/3001995589.py:170: ComplexWarning: Casting complex values to real discards the imaginary part 'ipr_eigenvector': float(ipr_eigenvector),
Starting the integration...Starting the integration...Starting the integration...Starting the integration... Starting the integration...Starting the integration...Starting the integration...Starting the integration... Computing graph 2/50... Integration finished. Linear algebra computations... Computations finished.
/tmp/ipykernel_1027/3001995589.py:160: ComplexWarning: Casting complex values to real discards the imaginary part 'critical_eigenvalue': float(eigenvalues[index_lambda_c]), /tmp/ipykernel_1027/3001995589.py:170: ComplexWarning: Casting complex values to real discards the imaginary part 'ipr_eigenvector': float(ipr_eigenvector),
Integration finished. Linear algebra computations... Computations finished. Integration finished. Linear algebra computations... Computations finished.
/tmp/ipykernel_1027/3001995589.py:160: ComplexWarning: Casting complex values to real discards the imaginary part 'critical_eigenvalue': float(eigenvalues[index_lambda_c]), /tmp/ipykernel_1027/3001995589.py:170: ComplexWarning: Casting complex values to real discards the imaginary part 'ipr_eigenvector': float(ipr_eigenvector),
Integration finished. Linear algebra computations... Computations finished. Integration finished. Linear algebra computations...Integration finished. Integration finished.Linear algebra computations... Linear algebra computations...Computations finished. Computations finished.
/tmp/ipykernel_1027/3001995589.py:160: ComplexWarning: Casting complex values to real discards the imaginary part 'critical_eigenvalue': float(eigenvalues[index_lambda_c]),
/tmp/ipykernel_1027/3001995589.py:170: ComplexWarning: Casting complex values to real discards the imaginary part 'ipr_eigenvector': float(ipr_eigenvector),
Computations finished.
/tmp/ipykernel_1027/3001995589.py:160: ComplexWarning: Casting complex values to real discards the imaginary part 'critical_eigenvalue': float(eigenvalues[index_lambda_c]), /tmp/ipykernel_1027/3001995589.py:170: ComplexWarning: Casting complex values to real discards the imaginary part 'ipr_eigenvector': float(ipr_eigenvector),
Integration finished. Linear algebra computations... Computations finished. Starting the integration...Starting the integration...Starting the integration... Starting the integration... Starting the integration...Starting the integration...Starting the integration...Starting the integration... Computing graph 3/50... Integration finished. Linear algebra computations...Integration finished. Linear algebra computations... Computations finished. Computations finished. Integration finished. Linear algebra computations... Integration finished.Computations finished. Linear algebra computations... Computations finished.Integration finished. Linear algebra computations... Integration finished. Computations finished.Linear algebra computations... Computations finished. Integration finished. Linear algebra computations... Integration finished.Computations finished. Linear algebra computations... Computations finished. Starting the integration...Starting the integration...Starting the integration... Starting the integration...Starting the integration...Starting the integration...Starting the integration...Starting the integration... Computing graph 4/50... Integration finished. Linear algebra computations... Computations finished. Integration finished.Integration finished. Linear algebra computations...Linear algebra computations... Computations finished.Integration finished.Computations finished. Linear algebra computations... Computations finished. Integration finished. Linear algebra computations... Computations finished. Integration finished. Linear algebra computations...Integration finished. Linear algebra computations...Computations finished. Computations finished.Integration finished. Linear algebra computations... Computations finished. Starting the integration...Starting the integration...Starting the integration...Starting the integration...Starting the integration...Starting the integration...Starting the integration... Starting the integration... Computing graph 5/50... Integration finished. Linear algebra computations... Computations finished. Integration finished. Linear algebra computations... Integration finished. Linear algebra computations...Computations finished. Integration finished. Computations finished.Linear algebra computations... Computations finished. Integration finished. Linear algebra computations... Computations finished. Integration finished. Linear algebra computations...Integration finished. Linear algebra computations... Computations finished. Computations finished. Integration finished. Linear algebra computations... Computations finished. Starting the integration...Starting the integration...Starting the integration...Starting the integration... Starting the integration...Starting the integration...Starting the integration... Starting the integration... Computing graph 6/50... Integration finished. Linear algebra computations... Computations finished. Integration finished.Integration finished. Linear algebra computations...Linear algebra computations... Computations finished.Computations finished. Integration finished. Linear algebra computations... Computations finished. Integration finished. Linear algebra computations... Computations finished. Integration finished. Linear algebra computations... Computations finished. Integration finished. Linear algebra computations... Computations finished. Integration finished. Linear algebra computations... Computations finished. Starting the integration...Starting the integration...Starting the integration...Starting the integration... Starting the integration...Starting the integration... Starting the integration...Starting the integration... Computing graph 7/50... Integration finished. Linear algebra computations... Computations finished. Integration finished. Linear algebra computations... Computations finished. Integration finished. Linear algebra computations... Computations finished. Integration finished. Linear algebra computations... Integration finished. Linear algebra computations...Integration finished.Computations finished. Linear algebra computations... Computations finished. Computations finished. Integration finished. Linear algebra computations... Computations finished. Integration finished. Linear algebra computations... Computations finished. Starting the integration...Starting the integration...Starting the integration... Starting the integration...Starting the integration...Starting the integration...Starting the integration...Starting the integration... Computing graph 8/50... Integration finished. Linear algebra computations... Computations finished. Integration finished. Linear algebra computations... Computations finished. Integration finished. Linear algebra computations... Computations finished. Integration finished. Linear algebra computations... Computations finished. Integration finished. Linear algebra computations... Integration finished.Computations finished. Linear algebra computations... Computations finished. Integration finished. Linear algebra computations... Computations finished.Integration finished. Linear algebra computations... Computations finished. Starting the integration...Starting the integration...Starting the integration...Starting the integration...Starting the integration... Starting the integration... Starting the integration...Starting the integration... Computing graph 9/50... Integration finished. Linear algebra computations... Integration finished.Computations finished. Linear algebra computations... Computations finished. Integration finished. Linear algebra computations... Computations finished. Integration finished. Linear algebra computations... Computations finished. Integration finished. Linear algebra computations... Computations finished. Integration finished. Linear algebra computations... Computations finished. Integration finished. Linear algebra computations... Computations finished. Integration finished. Linear algebra computations... Computations finished. Starting the integration...Starting the integration...Starting the integration...Starting the integration...Starting the integration...Starting the integration...Starting the integration...Starting the integration... Computing graph 10/50... Integration finished. Linear algebra computations... Computations finished. Integration finished. Linear algebra computations... Computations finished.Integration finished. Linear algebra computations... Computations finished. Integration finished. Linear algebra computations... Computations finished. Integration finished. Linear algebra computations... Computations finished. Integration finished. Linear algebra computations... Integration finished.Computations finished. Linear algebra computations... Computations finished. Integration finished. Linear algebra computations... Computations finished. Starting the integration...Starting the integration...Starting the integration...Starting the integration...Starting the integration... Starting the integration...Starting the integration...Starting the integration... Computing graph 11/50... Integration finished. Linear algebra computations... Computations finished. Integration finished. Linear algebra computations... Computations finished. Integration finished. Linear algebra computations... Computations finished. Integration finished. Linear algebra computations... Computations finished. Integration finished. Linear algebra computations... Computations finished. Integration finished. Linear algebra computations... Computations finished. Integration finished. Linear algebra computations... Computations finished. Integration finished. Linear algebra computations... Computations finished. Starting the integration...Starting the integration...Starting the integration...Starting the integration...Starting the integration...Starting the integration... Starting the integration... Starting the integration... Computing graph 12/50... Integration finished. Linear algebra computations... Computations finished. Integration finished. Linear algebra computations... Computations finished. Integration finished. Linear algebra computations... Computations finished. Integration finished. Linear algebra computations... Computations finished. Integration finished. Linear algebra computations... Computations finished. Integration finished. Linear algebra computations... Computations finished. Integration finished. Linear algebra computations... Computations finished. Integration finished. Linear algebra computations... Computations finished. Starting the integration...Starting the integration...Starting the integration...Starting the integration...Starting the integration...Starting the integration... Starting the integration...Starting the integration... Computing graph 13/50... Integration finished. Linear algebra computations... Computations finished. Integration finished. Linear algebra computations... Computations finished. Integration finished. Linear algebra computations... Computations finished. Integration finished.Integration finished. Linear algebra computations...Linear algebra computations... Computations finished.Computations finished. Integration finished. Linear algebra computations... Computations finished. Integration finished. Linear algebra computations...Integration finished. Linear algebra computations...Computations finished. Computations finished. Starting the integration...Starting the integration...Starting the integration...Starting the integration...Starting the integration...Starting the integration...Starting the integration...Starting the integration... Computing graph 14/50... Integration finished. Linear algebra computations... Computations finished. Integration finished. Linear algebra computations... Computations finished. Integration finished. Linear algebra computations... Computations finished. Integration finished. Linear algebra computations... Computations finished. Integration finished. Integration finished.Linear algebra computations... Linear algebra computations... Computations finished. Computations finished. Integration finished. Linear algebra computations... Computations finished. Integration finished. Linear algebra computations... Computations finished. Starting the integration...Starting the integration... Starting the integration...Starting the integration...Starting the integration...Starting the integration...Starting the integration...Starting the integration... Computing graph 15/50... Integration finished. Linear algebra computations... Computations finished. Integration finished. Linear algebra computations... Computations finished. Integration finished. Linear algebra computations... Computations finished. Integration finished. Linear algebra computations... Computations finished. Integration finished. Linear algebra computations... Computations finished. Integration finished. Linear algebra computations... Computations finished. Integration finished. Integration finished.Linear algebra computations... Linear algebra computations... Computations finished. Computations finished. Starting the integration...Starting the integration...Starting the integration...Starting the integration...Starting the integration... Starting the integration... Starting the integration...Starting the integration... Computing graph 16/50... Integration finished. Linear algebra computations... Computations finished. Integration finished. Linear algebra computations... Computations finished. Integration finished. Linear algebra computations... Computations finished. Integration finished. Linear algebra computations... Computations finished. Integration finished. Linear algebra computations... Integration finished.Computations finished. Linear algebra computations... Computations finished. Integration finished. Linear algebra computations... Computations finished. Integration finished. Linear algebra computations... Computations finished. Starting the integration...Starting the integration...Starting the integration...Starting the integration...Starting the integration...Starting the integration...Starting the integration... Starting the integration... Computing graph 17/50... Integration finished. Linear algebra computations... Computations finished. Integration finished. Linear algebra computations... Computations finished. Integration finished. Integration finished.Linear algebra computations... Linear algebra computations... Computations finished. Computations finished. Integration finished. Linear algebra computations... Computations finished. Integration finished. Linear algebra computations... Computations finished. Integration finished. Linear algebra computations...Integration finished. Linear algebra computations...Computations finished. Computations finished. Starting the integration...Starting the integration...Starting the integration...Starting the integration...Starting the integration...Starting the integration...Starting the integration... Starting the integration... Computing graph 18/50... Integration finished. Linear algebra computations... Computations finished. Integration finished. Linear algebra computations... Computations finished. Integration finished. Linear algebra computations... Computations finished. Integration finished. Linear algebra computations... Computations finished. Integration finished. Linear algebra computations... Computations finished. Integration finished. Linear algebra computations... Computations finished. Integration finished. Linear algebra computations... Computations finished.Integration finished. Linear algebra computations... Computations finished. Starting the integration...Starting the integration...Starting the integration...Starting the integration...Starting the integration...Starting the integration...Starting the integration... Starting the integration... Computing graph 19/50... Integration finished. Linear algebra computations... Computations finished. Integration finished. Linear algebra computations... Computations finished. Integration finished. Linear algebra computations... Computations finished. Integration finished. Linear algebra computations... Computations finished. Integration finished. Linear algebra computations... Computations finished. Integration finished. Linear algebra computations... Computations finished. Integration finished. Linear algebra computations... Computations finished. Integration finished. Linear algebra computations... Computations finished. Starting the integration...Starting the integration...Starting the integration...Starting the integration... Starting the integration... Starting the integration... Starting the integration...Starting the integration... Computing graph 20/50... Integration finished. Linear algebra computations... Computations finished. Integration finished. Linear algebra computations... Computations finished. Integration finished. Linear algebra computations... Computations finished. Integration finished. Linear algebra computations... Computations finished. Integration finished. Linear algebra computations... Computations finished. Integration finished. Integration finished.Linear algebra computations... Linear algebra computations... Computations finished.Computations finished. Integration finished. Linear algebra computations... Computations finished. Starting the integration...Starting the integration...Starting the integration...Starting the integration... Starting the integration... Starting the integration...Starting the integration... Starting the integration... Computing graph 21/50... Integration finished. Linear algebra computations... Computations finished. Integration finished. Linear algebra computations... Computations finished. Integration finished. Linear algebra computations... Computations finished. Integration finished. Linear algebra computations... Computations finished. Integration finished. Linear algebra computations... Computations finished.Integration finished. Linear algebra computations... Computations finished. Integration finished. Linear algebra computations... Computations finished. Integration finished. Linear algebra computations... Computations finished. Starting the integration...Starting the integration...Starting the integration...Starting the integration...Starting the integration... Starting the integration...Starting the integration... Starting the integration... Computing graph 22/50... Integration finished. Linear algebra computations... Computations finished. Integration finished. Linear algebra computations... Computations finished. Integration finished. Linear algebra computations... Computations finished. Integration finished. Linear algebra computations... Integration finished. Computations finished.Linear algebra computations... Computations finished. Integration finished. Linear algebra computations... Computations finished. Integration finished. Linear algebra computations... Computations finished. Integration finished. Linear algebra computations... Computations finished. Starting the integration...Starting the integration... Starting the integration...Starting the integration...Starting the integration... Starting the integration... Starting the integration...Starting the integration... Computing graph 23/50... Integration finished. Linear algebra computations... Computations finished. Integration finished. Linear algebra computations... Computations finished. Integration finished. Linear algebra computations... Integration finished. Linear algebra computations...Computations finished.Integration finished. Linear algebra computations...Computations finished. Computations finished. Integration finished. Linear algebra computations... Integration finished.Computations finished. Linear algebra computations... Computations finished. Integration finished. Linear algebra computations... Computations finished. Starting the integration...Starting the integration...Starting the integration...Starting the integration...Starting the integration...Starting the integration...Starting the integration... Starting the integration... Computing graph 24/50... Integration finished. Linear algebra computations... Computations finished. Integration finished. Linear algebra computations... Computations finished. Integration finished. Linear algebra computations... Computations finished. Integration finished. Linear algebra computations... Computations finished. Integration finished. Linear algebra computations... Computations finished. Integration finished. Linear algebra computations... Computations finished. Integration finished. Linear algebra computations... Computations finished. Integration finished. Linear algebra computations... Computations finished. Starting the integration...Starting the integration...Starting the integration...Starting the integration... Starting the integration...Starting the integration... Starting the integration... Starting the integration... Computing graph 25/50... Integration finished. Linear algebra computations... Computations finished. Integration finished. Linear algebra computations... Computations finished. Integration finished. Linear algebra computations... Computations finished. Integration finished. Linear algebra computations... Computations finished. Integration finished. Integration finished.Linear algebra computations... Linear algebra computations... Computations finished. Computations finished. Integration finished. Linear algebra computations... Computations finished. Integration finished. Linear algebra computations... Computations finished. Starting the integration...Starting the integration...Starting the integration...Starting the integration...Starting the integration...Starting the integration...Starting the integration... Starting the integration... Computing graph 26/50... Integration finished. Linear algebra computations... Computations finished. Integration finished. Linear algebra computations... Computations finished. Integration finished. Linear algebra computations... Computations finished. Integration finished. Linear algebra computations... Computations finished. Integration finished. Linear algebra computations... Integration finished.Computations finished. Linear algebra computations... Computations finished. Integration finished. Linear algebra computations... Computations finished. Integration finished. Linear algebra computations... Computations finished. Starting the integration...Starting the integration...Starting the integration...Starting the integration...Starting the integration... Starting the integration... Starting the integration... Starting the integration... Computing graph 27/50... Integration finished. Linear algebra computations... Computations finished. Integration finished. Linear algebra computations... Computations finished. Integration finished. Linear algebra computations... Computations finished. Integration finished. Linear algebra computations... Computations finished. Integration finished. Linear algebra computations... Computations finished. Integration finished. Linear algebra computations... Computations finished. Integration finished. Linear algebra computations... Computations finished. Integration finished. Linear algebra computations... Computations finished. Starting the integration...Starting the integration...Starting the integration... Starting the integration...Starting the integration...Starting the integration...Starting the integration...Starting the integration... Computing graph 28/50... Integration finished. Linear algebra computations... Computations finished. Integration finished. Linear algebra computations... Computations finished. Integration finished. Linear algebra computations... Computations finished. Integration finished. Linear algebra computations... Computations finished. Integration finished. Linear algebra computations... Computations finished. Integration finished. Linear algebra computations... Computations finished. Integration finished. Linear algebra computations... Computations finished. Integration finished. Linear algebra computations... Computations finished. Starting the integration...Starting the integration...Starting the integration... Starting the integration...Starting the integration...Starting the integration... Starting the integration...Starting the integration... Computing graph 29/50... Integration finished. Linear algebra computations... Computations finished. Integration finished. Linear algebra computations... Computations finished. Integration finished. Linear algebra computations...Integration finished. Linear algebra computations... Computations finished. Computations finished. Integration finished. Linear algebra computations... Computations finished. Integration finished. Linear algebra computations... Computations finished. Integration finished. Linear algebra computations... Computations finished. Integration finished. Linear algebra computations... Computations finished. Starting the integration...Starting the integration...Starting the integration... Starting the integration...Starting the integration...Starting the integration...Starting the integration... Starting the integration... Computing graph 30/50... Integration finished. Linear algebra computations... Computations finished. Integration finished.Integration finished. Linear algebra computations...Linear algebra computations... Computations finished. Computations finished. Integration finished. Linear algebra computations... Computations finished. Integration finished. Linear algebra computations... Computations finished. Integration finished. Linear algebra computations... Computations finished. Integration finished. Linear algebra computations... Computations finished. Integration finished. Linear algebra computations... Computations finished. Starting the integration...Starting the integration...Starting the integration...Starting the integration...Starting the integration... Starting the integration...Starting the integration...Starting the integration... Computing graph 31/50... Integration finished. Linear algebra computations... Computations finished. Integration finished. Linear algebra computations...Integration finished. Linear algebra computations... Computations finished. Computations finished. Integration finished. Linear algebra computations... Computations finished. Integration finished. Linear algebra computations... Computations finished. Integration finished.Integration finished. Linear algebra computations...Linear algebra computations... Computations finished.Computations finished. Integration finished. Linear algebra computations... Computations finished. Starting the integration...Starting the integration...Starting the integration...Starting the integration...Starting the integration...Starting the integration... Starting the integration...Starting the integration... Computing graph 32/50... Integration finished. Linear algebra computations... Computations finished. Integration finished. Linear algebra computations... Computations finished. Integration finished. Linear algebra computations... Computations finished. Integration finished. Linear algebra computations... Computations finished. Integration finished. Linear algebra computations... Computations finished. Integration finished. Integration finished.Linear algebra computations... Linear algebra computations... Computations finished. Computations finished. Integration finished. Linear algebra computations... Computations finished. Starting the integration...Starting the integration... Starting the integration...Starting the integration...Starting the integration...Starting the integration...Starting the integration...Starting the integration... Computing graph 33/50... Integration finished. Linear algebra computations... Computations finished. Integration finished. Linear algebra computations... Computations finished. Integration finished. Linear algebra computations... Computations finished. Integration finished. Linear algebra computations... Computations finished. Integration finished. Integration finished.Linear algebra computations... Linear algebra computations... Computations finished. Computations finished. Integration finished. Linear algebra computations... Computations finished. Integration finished. Linear algebra computations... Computations finished. Starting the integration...Starting the integration...Starting the integration...Starting the integration...Starting the integration...Starting the integration... Starting the integration...Starting the integration... Computing graph 34/50... Integration finished. Linear algebra computations... Computations finished. Integration finished. Integration finished.Linear algebra computations... Linear algebra computations... Computations finished. Computations finished. Integration finished. Linear algebra computations... Computations finished. Integration finished. Linear algebra computations... Computations finished. Integration finished. Linear algebra computations... Computations finished. Integration finished. Linear algebra computations... Integration finished.Computations finished. Linear algebra computations... Computations finished. Starting the integration...Starting the integration...Starting the integration...Starting the integration...Starting the integration...Starting the integration...Starting the integration... Starting the integration... Computing graph 35/50... Integration finished. Linear algebra computations... Computations finished. Integration finished. Linear algebra computations... Computations finished. Integration finished. Linear algebra computations... Computations finished. Integration finished. Linear algebra computations... Computations finished. Integration finished. Linear algebra computations... Computations finished. Integration finished. Linear algebra computations... Computations finished. Integration finished. Linear algebra computations... Computations finished. Integration finished. Linear algebra computations... Computations finished. Starting the integration...Starting the integration...Starting the integration...Starting the integration...Starting the integration... Starting the integration...Starting the integration...Starting the integration... Computing graph 36/50... Integration finished. Linear algebra computations... Computations finished. Integration finished. Linear algebra computations... Computations finished. Integration finished. Linear algebra computations... Computations finished. Integration finished. Linear algebra computations... Computations finished. Integration finished. Linear algebra computations... Computations finished. Integration finished. Linear algebra computations... Computations finished. Integration finished. Linear algebra computations... Computations finished. Integration finished. Linear algebra computations... Computations finished. Starting the integration...Starting the integration... Starting the integration...Starting the integration...Starting the integration...Starting the integration...Starting the integration...Starting the integration... Computing graph 37/50... Integration finished. Linear algebra computations... Computations finished. Integration finished. Linear algebra computations... Computations finished. Integration finished. Linear algebra computations... Computations finished. Integration finished. Linear algebra computations... Computations finished. Integration finished. Linear algebra computations... Computations finished. Integration finished. Linear algebra computations... Computations finished. Integration finished. Linear algebra computations... Computations finished. Integration finished. Linear algebra computations... Computations finished. Starting the integration...Starting the integration...Starting the integration...Starting the integration... Starting the integration...Starting the integration...Starting the integration...Starting the integration... Computing graph 38/50... Integration finished. Linear algebra computations... Computations finished. Integration finished. Linear algebra computations... Computations finished. Integration finished. Linear algebra computations... Computations finished. Integration finished. Linear algebra computations... Integration finished. Linear algebra computations...Computations finished. Computations finished. Integration finished. Linear algebra computations... Computations finished. Integration finished. Linear algebra computations... Computations finished. Integration finished. Linear algebra computations... Computations finished. Starting the integration...Starting the integration...Starting the integration...Starting the integration...Starting the integration...Starting the integration... Starting the integration... Starting the integration... Computing graph 39/50... Integration finished. Linear algebra computations... Computations finished. Integration finished.Integration finished. Linear algebra computations...Linear algebra computations... Computations finished.Computations finished. Integration finished. Linear algebra computations... Computations finished. Integration finished. Integration finished.Linear algebra computations... Linear algebra computations... Computations finished. Computations finished. Integration finished. Linear algebra computations... Computations finished. Integration finished. Linear algebra computations... Computations finished. Starting the integration...Starting the integration...Starting the integration...Starting the integration... Starting the integration...Starting the integration... Starting the integration...Starting the integration... Computing graph 40/50... Integration finished. Linear algebra computations... Computations finished. Integration finished. Linear algebra computations... Computations finished. Integration finished. Linear algebra computations... Computations finished.Integration finished. Linear algebra computations... Computations finished. Integration finished. Linear algebra computations... Computations finished. Integration finished. Linear algebra computations... Computations finished. Integration finished. Linear algebra computations... Computations finished. Integration finished. Linear algebra computations... Computations finished. Starting the integration...Starting the integration...Starting the integration...Starting the integration...Starting the integration...Starting the integration... Starting the integration... Starting the integration... Computing graph 41/50... Integration finished. Linear algebra computations... Integration finished.Computations finished. Linear algebra computations... Computations finished. Integration finished. Linear algebra computations... Computations finished. Integration finished. Linear algebra computations... Computations finished. Integration finished. Linear algebra computations... Computations finished. Integration finished. Linear algebra computations... Computations finished. Integration finished. Linear algebra computations... Computations finished. Integration finished. Linear algebra computations... Computations finished. Starting the integration...Starting the integration...Starting the integration...Starting the integration...Starting the integration... Starting the integration...Starting the integration... Starting the integration... Computing graph 42/50... Integration finished. Linear algebra computations... The critical eigenvalue is not in the range of the dispersion relation. The linear analysis cannot be performed. The critical eigenvalue is: -2.407968440118764
/tmp/ipykernel_1027/3001995589.py:147: RuntimeWarning: invalid value encountered in scalar divide ipr_eigenvector = np.sum(critical_eigenvector**4) / (np.sum(critical_eigenvector**2)**2)
Computations finished. Integration finished. Linear algebra computations... Computations finished. Integration finished. Linear algebra computations... Computations finished. Integration finished. Linear algebra computations... Computations finished. Integration finished. Linear algebra computations... The critical eigenvalue is not in the range of the dispersion relation. The linear analysis cannot be performed. The critical eigenvalue is: -2.3169223386273403
/tmp/ipykernel_1027/3001995589.py:147: RuntimeWarning: invalid value encountered in scalar divide ipr_eigenvector = np.sum(critical_eigenvector**4) / (np.sum(critical_eigenvector**2)**2)
Computations finished. Integration finished. Linear algebra computations... Computations finished. Integration finished. Linear algebra computations... Computations finished. Integration finished. Linear algebra computations... Computations finished. Starting the integration...Starting the integration...Starting the integration...Starting the integration...Starting the integration...Starting the integration... Starting the integration... Starting the integration... Computing graph 43/50... Integration finished. Linear algebra computations... Integration finished. Linear algebra computations...Computations finished. The critical eigenvalue is not in the range of the dispersion relation. The linear analysis cannot be performed. The critical eigenvalue is: Integration finished. -2.4972330430819487 Linear algebra computations...
/tmp/ipykernel_1027/3001995589.py:147: RuntimeWarning: invalid value encountered in scalar divide ipr_eigenvector = np.sum(critical_eigenvector**4) / (np.sum(critical_eigenvector**2)**2)
Computations finished. The critical eigenvalue is not in the range of the dispersion relation. The linear analysis cannot be performed. The critical eigenvalue is: -2.272325315368397
/tmp/ipykernel_1027/3001995589.py:147: RuntimeWarning: invalid value encountered in scalar divide ipr_eigenvector = np.sum(critical_eigenvector**4) / (np.sum(critical_eigenvector**2)**2)
Computations finished. Integration finished. Linear algebra computations... The critical eigenvalue is not in the range of the dispersion relation. The linear analysis cannot be performed. The critical eigenvalue is: -2.2548615863376638
/tmp/ipykernel_1027/3001995589.py:147: RuntimeWarning: invalid value encountered in scalar divide ipr_eigenvector = np.sum(critical_eigenvector**4) / (np.sum(critical_eigenvector**2)**2)
Computations finished. Integration finished. Linear algebra computations... The critical eigenvalue is not in the range of the dispersion relation. The linear analysis cannot be performed. The critical eigenvalue is: -2.68406466817104 Computations finished. Integration finished. Linear algebra computations... Computations finished. Integration finished. Linear algebra computations... The critical eigenvalue is not in the range of the dispersion relation. The linear analysis cannot be performed. The critical eigenvalue is: -2.4340214168083305
/tmp/ipykernel_1027/3001995589.py:147: RuntimeWarning: invalid value encountered in scalar divide ipr_eigenvector = np.sum(critical_eigenvector**4) / (np.sum(critical_eigenvector**2)**2)
Computations finished. Integration finished. Linear algebra computations... The critical eigenvalue is not in the range of the dispersion relation. The linear analysis cannot be performed. The critical eigenvalue is: -2.2882658402642044
/tmp/ipykernel_1027/3001995589.py:147: RuntimeWarning: invalid value encountered in scalar divide ipr_eigenvector = np.sum(critical_eigenvector**4) / (np.sum(critical_eigenvector**2)**2)
Computations finished. Starting the integration...Starting the integration...Starting the integration...Starting the integration...Starting the integration...Starting the integration...Starting the integration...Starting the integration... Computing graph 44/50... Integration finished. Linear algebra computations... The critical eigenvalue is not in the range of the dispersion relation. The linear analysis cannot be performed. The critical eigenvalue is: -2.8265810535668106 Computations finished. Integration finished. Linear algebra computations... Integration finished.The critical eigenvalue is not in the range of the dispersion relation. The linear analysis cannot be performed.Linear algebra computations... The critical eigenvalue is: The critical eigenvalue is not in the range of the dispersion relation.-2.58979352102367 The linear analysis cannot be performed.Computations finished. The critical eigenvalue is: -2.777485888506203 Computations finished. Integration finished. Linear algebra computations... The critical eigenvalue is not in the range of the dispersion relation. The linear analysis cannot be performed. The critical eigenvalue is: 1.3322676295501878e-15
/tmp/ipykernel_1027/3001995589.py:147: RuntimeWarning: invalid value encountered in scalar divide ipr_eigenvector = np.sum(critical_eigenvector**4) / (np.sum(critical_eigenvector**2)**2)
Computations finished. Integration finished. Linear algebra computations... The critical eigenvalue is not in the range of the dispersion relation. The linear analysis cannot be performed. The critical eigenvalue is: -2.7995255566177097
/tmp/ipykernel_1027/3001995589.py:147: RuntimeWarning: invalid value encountered in scalar divide ipr_eigenvector = np.sum(critical_eigenvector**4) / (np.sum(critical_eigenvector**2)**2)
Computations finished. Integration finished. Linear algebra computations... The critical eigenvalue is not in the range of the dispersion relation. The linear analysis cannot be performed. The critical eigenvalue is: 1.3322676295501878e-15
/tmp/ipykernel_1027/3001995589.py:147: RuntimeWarning: invalid value encountered in scalar divide ipr_eigenvector = np.sum(critical_eigenvector**4) / (np.sum(critical_eigenvector**2)**2)
Computations finished. Integration finished. Linear algebra computations... The critical eigenvalue is not in the range of the dispersion relation. The linear analysis cannot be performed. The critical eigenvalue is: Integration finished. 4.440892098500626e-16Linear algebra computations... Computations finished. The critical eigenvalue is not in the range of the dispersion relation. The linear analysis cannot be performed. The critical eigenvalue is: 8.881784197001252e-16
/tmp/ipykernel_1027/3001995589.py:147: RuntimeWarning: invalid value encountered in scalar divide ipr_eigenvector = np.sum(critical_eigenvector**4) / (np.sum(critical_eigenvector**2)**2)
Computations finished. Starting the integration...Starting the integration...Starting the integration...Starting the integration...Starting the integration...Starting the integration...Starting the integration...Starting the integration... Computing graph 45/50... Integration finished. Linear algebra computations... The critical eigenvalue is not in the range of the dispersion relation. The linear analysis cannot be performed. The critical eigenvalue is: -1.7763568394002505e-15 Computations finished. Integration finished. Linear algebra computations... The critical eigenvalue is not in the range of the dispersion relation. The linear analysis cannot be performed. The critical eigenvalue is: Integration finished. 8.881784197001252e-16Linear algebra computations... Computations finished. The critical eigenvalue is not in the range of the dispersion relation. The linear analysis cannot be performed. The critical eigenvalue is: 4.440892098500626e-16 Computations finished. Integration finished. Linear algebra computations... The critical eigenvalue is not in the range of the dispersion relation. The linear analysis cannot be performed. The critical eigenvalue is: -1.3322676295501878e-15 Computations finished. Integration finished. Linear algebra computations... The critical eigenvalue is not in the range of the dispersion relation. The linear analysis cannot be performed. The critical eigenvalue is: 8.881784197001252e-16 Computations finished. Integration finished. Linear algebra computations... The critical eigenvalue is not in the range of the dispersion relation. The linear analysis cannot be performed. The critical eigenvalue is: 1.7763568394002505e-15
/tmp/ipykernel_1027/3001995589.py:147: RuntimeWarning: invalid value encountered in scalar divide ipr_eigenvector = np.sum(critical_eigenvector**4) / (np.sum(critical_eigenvector**2)**2)
Computations finished. Integration finished. Linear algebra computations... The critical eigenvalue is not in the range of the dispersion relation. The linear analysis cannot be performed. The critical eigenvalue is: -8.881784197001252e-16 Computations finished.Integration finished. Linear algebra computations... The critical eigenvalue is not in the range of the dispersion relation. The linear analysis cannot be performed. The critical eigenvalue is: 5.810106010205084e-16 Computations finished. Starting the integration...Starting the integration...Starting the integration...Starting the integration...Starting the integration...Starting the integration...Starting the integration...Starting the integration... Computing graph 46/50... Integration finished. Linear algebra computations... The critical eigenvalue is not in the range of the dispersion relation. The linear analysis cannot be performed. The critical eigenvalue is: -8.881784197001252e-16 Computations finished. Integration finished. Linear algebra computations... The critical eigenvalue is not in the range of the dispersion relation. The linear analysis cannot be performed. The critical eigenvalue is: 8.881784197001252e-16 Computations finished. Integration finished. Linear algebra computations... The critical eigenvalue is not in the range of the dispersion relation. The linear analysis cannot be performed. The critical eigenvalue is: 0.0 Computations finished. Integration finished. Linear algebra computations... The critical eigenvalue is not in the range of the dispersion relation. The linear analysis cannot be performed. The critical eigenvalue is: Integration finished. -1.5044397281716031e-15Linear algebra computations... Computations finished. The critical eigenvalue is not in the range of the dispersion relation. The linear analysis cannot be performed. The critical eigenvalue is: -3.552713678800501e-15 Computations finished. Integration finished. Linear algebra computations... The critical eigenvalue is not in the range of the dispersion relation. The linear analysis cannot be performed. The critical eigenvalue is: 1.7763568394002505e-15 Computations finished. Integration finished. Linear algebra computations... The critical eigenvalue is not in the range of the dispersion relation. The linear analysis cannot be performed. The critical eigenvalue is: Integration finished. 4.440892098500626e-16Linear algebra computations... Computations finished. The critical eigenvalue is not in the range of the dispersion relation. The linear analysis cannot be performed. The critical eigenvalue is: 1.7763568394002505e-15 Computations finished. Starting the integration...Starting the integration...Starting the integration...Starting the integration...Starting the integration... Starting the integration...Starting the integration...Starting the integration... Computing graph 47/50... Integration finished. Linear algebra computations... The critical eigenvalue is not in the range of the dispersion relation. The linear analysis cannot be performed. The critical eigenvalue is: -1.7763568394002505e-15 Computations finished. Integration finished. Linear algebra computations... The critical eigenvalue is not in the range of the dispersion relation. The linear analysis cannot be performed. The critical eigenvalue is: -2.0567257790018154e-15 Computations finished. Integration finished. Linear algebra computations... The critical eigenvalue is not in the range of the dispersion relation. The linear analysis cannot be performed. The critical eigenvalue is: -3.2125298715835343e-15 Computations finished. Integration finished. Linear algebra computations... The critical eigenvalue is not in the range of the dispersion relation. The linear analysis cannot be performed. The critical eigenvalue is: 0.0 Computations finished. Integration finished. Linear algebra computations... The critical eigenvalue is not in the range of the dispersion relation. The linear analysis cannot be performed. The critical eigenvalue is: 8.881784197001252e-16 Computations finished. Integration finished. Linear algebra computations... The critical eigenvalue is not in the range of the dispersion relation. The linear analysis cannot be performed. The critical eigenvalue is: 1.8754757027629315e-15 Computations finished. Integration finished. Linear algebra computations... The critical eigenvalue is not in the range of the dispersion relation. The linear analysis cannot be performed. The critical eigenvalue is: -1.0676877769707976e-15 Computations finished. Integration finished. Linear algebra computations... The critical eigenvalue is not in the range of the dispersion relation. The linear analysis cannot be performed. The critical eigenvalue is: -1.7763568394002505e-15 Computations finished. Starting the integration...Starting the integration...Starting the integration...Starting the integration...Starting the integration... Starting the integration... Starting the integration...Starting the integration... Computing graph 48/50... Integration finished. Linear algebra computations... The critical eigenvalue is not in the range of the dispersion relation. The linear analysis cannot be performed. The critical eigenvalue is: -1.6630936661505222e-15 Computations finished. Integration finished. Linear algebra computations... The critical eigenvalue is not in the range of the dispersion relation. The linear analysis cannot be performed. The critical eigenvalue is: -6.168085144480596e-16 Computations finished. Integration finished. Linear algebra computations... The critical eigenvalue is not in the range of the dispersion relation. The linear analysis cannot be performed. The critical eigenvalue is: -1.8374154189959897e-15 Computations finished. Integration finished. Linear algebra computations... The critical eigenvalue is not in the range of the dispersion relation. The linear analysis cannot be performed. The critical eigenvalue is: 0.0 Computations finished. Integration finished. Linear algebra computations... The critical eigenvalue is not in the range of the dispersion relation. The linear analysis cannot be performed. The critical eigenvalue is: 2.6645352591003757e-15 Computations finished. Integration finished. Linear algebra computations... The critical eigenvalue is not in the range of the dispersion relation. The linear analysis cannot be performed. The critical eigenvalue is: -1.7232489678676572e-15 Computations finished. Integration finished. Linear algebra computations...Integration finished. Linear algebra computations... The critical eigenvalue is not in the range of the dispersion relation. The linear analysis cannot be performed.The critical eigenvalue is not in the range of the dispersion relation. The critical eigenvalue is: The linear analysis cannot be performed. 9.705552083232977e-16The critical eigenvalue is: Computations finished.-8.881784197001252e-16 Computations finished. Starting the integration...Starting the integration...Starting the integration...Starting the integration...Starting the integration...Starting the integration... Starting the integration...Starting the integration... Computing graph 49/50... Integration finished. Linear algebra computations... The critical eigenvalue is not in the range of the dispersion relation. The linear analysis cannot be performed. The critical eigenvalue is: -2.7865462195338268e-15 Computations finished. Integration finished. Linear algebra computations... The critical eigenvalue is not in the range of the dispersion relation. The linear analysis cannot be performed. The critical eigenvalue is: 3.1079364088969327e-15 Computations finished. Integration finished. Linear algebra computations... The critical eigenvalue is not in the range of the dispersion relation. The linear analysis cannot be performed. The critical eigenvalue is: 4.440892098500626e-15 Computations finished. Integration finished. Linear algebra computations... The critical eigenvalue is not in the range of the dispersion relation. The linear analysis cannot be performed. The critical eigenvalue is: -1.0128582962932408e-15 Computations finished. Integration finished. Linear algebra computations... The critical eigenvalue is not in the range of the dispersion relation. The linear analysis cannot be performed. The critical eigenvalue is: 2.7698237345273254e-16 Computations finished. Integration finished. Linear algebra computations... The critical eigenvalue is not in the range of the dispersion relation. The linear analysis cannot be performed. The critical eigenvalue is: Integration finished. 8.881784197001252e-16Linear algebra computations... Computations finished. The critical eigenvalue is not in the range of the dispersion relation. The linear analysis cannot be performed. The critical eigenvalue is: 0.0 Computations finished. Integration finished. Linear algebra computations... The critical eigenvalue is not in the range of the dispersion relation. The linear analysis cannot be performed. The critical eigenvalue is: -3.4120797654081527e-15 Computations finished. Starting the integration...Starting the integration...Starting the integration...Starting the integration... Starting the integration...Starting the integration...Starting the integration... Starting the integration... Computing graph 50/50... Integration finished. Linear algebra computations... The critical eigenvalue is not in the range of the dispersion relation. The linear analysis cannot be performed. The critical eigenvalue is: 2.8118598154984204e-15 Computations finished. Integration finished. Linear algebra computations... The critical eigenvalue is not in the range of the dispersion relation. The linear analysis cannot be performed. The critical eigenvalue is: -1.1397156435696196e-15 Computations finished. Integration finished. Linear algebra computations... The critical eigenvalue is not in the range of the dispersion relation. The linear analysis cannot be performed. The critical eigenvalue is: 6.580620990714174e-15Integration finished. Computations finished.Linear algebra computations... The critical eigenvalue is not in the range of the dispersion relation. The linear analysis cannot be performed. The critical eigenvalue is: -4.808412112914714e-15 Computations finished. Integration finished. Linear algebra computations... The critical eigenvalue is not in the range of the dispersion relation. The linear analysis cannot be performed. The critical eigenvalue is: -8.881784197001252e-16 Computations finished. Integration finished. Linear algebra computations... The critical eigenvalue is not in the range of the dispersion relation. The linear analysis cannot be performed. The critical eigenvalue is: -2.227648577984641e-15 Computations finished. Integration finished. Linear algebra computations... The critical eigenvalue is not in the range of the dispersion relation. The linear analysis cannot be performed. The critical eigenvalue is: -5.807892406662716e-16 Computations finished. Integration finished. Linear algebra computations... The critical eigenvalue is not in the range of the dispersion relation. The linear analysis cannot be performed. The critical eigenvalue is: 5.57723272274762e-16 Computations finished. Plotting the results...
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0.024999999999999998], [0.025000000000000012, 0.025000000000000012, 0.025000000000000012, 0.025000000000000012, 0.025000000000000012, 0.025000000000000012, 0.025000000000000012, 0.024999999999999998], [0.025000000000000012, 0.025000000000000012, 0.025000000000000012, 0.025000000000000012, 0.025000000000000012, 0.025000000000000012, 0.025000000000000012, 0.024999999999999998], [0.025000000000000012, 0.025000000000000012, 0.025000000000000012, 0.025000000000000012, 0.025000000000000012, 0.025000000000000012, 0.025, 0.024999999999999998], [0.025000000000000012, 0.025000000000000012, 0.025000000000000012, 0.025000000000000012, 0.025000000000000012, 0.025000000000000012, 0.025, 0.024999999999999998], [0.025000000000000012, 0.025000000000000012, 0.025000000000000012, 0.025000000000000012, 0.025000000000000012, 0.025000000000000012, 0.025, 0.024999999999999998], [0.025000000000000012, 0.025000000000000012, 0.025000000000000012, 0.025000000000000012, 0.025000000000000012, 0.025000000000000012, 0.025, 0.024999999999999998], [0.025000000000000005, 0.025000000000000012, 0.025000000000000012, 0.025000000000000012, 0.025000000000000012, 0.025000000000000012, 0.025, 0.024999999999999998], [0.025000000000000005, 0.025000000000000012, 0.025000000000000012, 0.025000000000000012, 0.025000000000000012, 0.025000000000000012, 0.025, 0.024999999999999998], [0.025000000000000005, 0.025000000000000012, 0.025000000000000012, 0.025000000000000012, 0.025000000000000012, 0.025000000000000012, 0.025, 0.024999999999999998], [0.025000000000000005, 0.025000000000000012, 0.025000000000000012, 0.025000000000000012, 0.025000000000000012, 0.025, 0.025, 0.024999999999999998], [0.025000000000000005, 0.025, 0.025000000000000012, 0.025000000000000012, 0.025000000000000012, 0.025, 0.025, 0.024999999999999998], [0.025000000000000005, 0.025, 0.025000000000000012, 0.025000000000000012, 0.025000000000000012, 0.025, 0.025, 0.024999999999999998], [0.025000000000000005, 0.025, 0.025000000000000012, 0.025000000000000012, 0.025000000000000012, 0.025, 0.025, 0.024999999999999998], [0.025000000000000005, 0.025, 0.025000000000000012, 0.025000000000000012, 0.025000000000000012, 0.025, 0.025, 0.025000000000000005], [0.025000000000000005, 0.025, 0.025000000000000012, 0.025000000000000012, 0.025000000000000012, 0.025, 0.025, 0.025000000000000005], [0.025000000000000005, 0.025, 0.025000000000000012, 0.025000000000000012, 0.025000000000000012, 0.025, 0.025, 0.025000000000000005], [0.025000000000000005, 0.025, 0.025000000000000012, 0.025000000000000012, 0.025000000000000012, 0.025, 0.025, 0.025000000000000005], [0.025000000000000005, 0.025, 0.025000000000000012, 0.025000000000000012, 0.025000000000000012, 0.025, 0.025, 0.025000000000000005], [0.025000000000000005, 0.025000000000000012, 0.025000000000000012, 0.025000000000000012, 0.025000000000000005, 0.025, 0.025, 0.025000000000000005], [0.025, 0.024999999999999994, 0.025000000000000012, 0.024999999999999994, 0.025000000000000005, 0.024999999999999998, 0.025, 0.025000000000000005], [0.024999999999999998, 0.024999999999999998, 0.025000000000000012, 0.024999999999999994, 0.025000000000000005, 0.024999999999999998, 0.02499999999999999, 0.025000000000000005], [0.025, 0.024999999999999994, 0.025, 0.024999999999999994, 0.025000000000000005, 0.024999999999999998, 0.025, 0.025000000000000005], [0.024999999999999998, 0.025000000000000005, 0.024999999999999998, 0.025, 0.025000000000000005, 0.025000000000000005, 0.025000000000000005, 0.024999999999999994], [0.025000000000000005, 0.025000000000000005, 0.025000000000000005, 0.024999999999999994, 0.025000000000000005, 0.025000000000000005, 0.025000000000000005, 0.024999999999999994], [0.025, 0.024999999999999998, 0.025000000000000005, 0.024999999999999994, 0.025000000000000005, 0.024999999999999994, 0.025, 0.024999999999999994], [0.025, 0.025000000000000005, 0.025, 0.024999999999999994, 0.025, 0.025, 0.025, 0.025], [0.025, 0.025000000000000005, 0.02499999999999999, 0.025000000000000005, 0.024999999999999998, 0.025, 0.025, 0.025], [0.025, 0.025000000000000005, 0.025, 0.025000000000000005, 0.025, 0.025, 0.025, 0.025], [0.024999999999999994, 0.025000000000000005, 0.025, 0.025, 0.025, 0.025, 0.025, 0.025000000000000005], [0.025, 0.025000000000000005, 0.025, 0.025, 0.025, 0.02499999999999999, 0.024999999999999994, 0.024999999999999994], [0.024999999999999994, 0.025, 0.024999999999999994, 0.025000000000000005, 0.025, 0.025000000000000005, 0.025, 0.02499999999999999], [0.025, 0.025, 0.025, 0.025, 0.024999999999999998, 0.024999999999999998, 0.024999999999999994, 0.025], [0.025000000000000005, 0.025, 0.025000000000000005, 0.024999999999999994, 0.025, 0.025, 0.024999999999999998, 0.024999999999999998], [0.025000000000000012, 0.024999999999999994, 0.025, 0.024999999999999998, 0.025, 0.024999999999999998, 0.025000000000000005, 0.025000000000000005], [0.025, 0.025, 0.024999999999999998, 0.025, 0.0, 0.025, 0.024999999999999994, 0.0], [0.025, 0.0, 0.0, 0.0, 0.0, 0.024999999999999994, 0.0, 0.0], [0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0], [0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0], [0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0], [0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0], [0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0], [0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0], [0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0]], 'data_k_avg': [[8.0, 8.0, 8.0, 8.0, 8.0, 8.0, 8.0, 8.0], [8.0, 8.0, 8.0, 8.0, 8.0, 8.0, 8.0, 8.0], [8.0, 8.0, 8.0, 8.0, 8.0, 8.0, 8.0, 8.0], [8.0, 8.0, 8.0, 8.0, 8.0, 8.0, 8.0, 8.0], [8.0, 8.0, 8.0, 8.0, 8.0, 8.0, 8.0, 8.0], [8.0, 8.0, 8.0, 8.0, 8.0, 8.0, 8.0, 8.05], [8.0, 8.0, 8.0, 8.0, 8.0, 8.0, 8.0, 8.05], [8.0, 8.0, 8.0, 8.0, 8.0, 8.0, 8.0, 8.05], [8.0, 8.0, 8.0, 8.0, 8.0, 8.0, 8.0, 8.05], [8.0, 8.0, 8.0, 8.0, 8.0, 8.0, 8.05, 8.05], [8.0, 8.0, 8.0, 8.0, 8.0, 8.0, 8.05, 8.05], [8.0, 8.0, 8.0, 8.0, 8.0, 8.0, 8.05, 8.05], [8.0, 8.0, 8.0, 8.0, 8.0, 8.0, 8.05, 8.05], [8.05, 8.0, 8.0, 8.0, 8.0, 8.0, 8.05, 8.05], [8.05, 8.0, 8.0, 8.0, 8.0, 8.0, 8.05, 8.05], [8.05, 8.0, 8.0, 8.0, 8.0, 8.0, 8.05, 8.05], [8.05, 8.0, 8.0, 8.0, 8.0, 8.05, 8.05, 8.05], [8.05, 8.1, 8.0, 8.0, 8.0, 8.05, 8.05, 8.05], [8.05, 8.1, 8.0, 8.0, 8.0, 8.05, 8.05, 8.05], [8.05, 8.1, 8.0, 8.0, 8.0, 8.05, 8.05, 8.05], [8.05, 8.1, 8.0, 8.0, 8.0, 8.05, 8.05, 8.1], [8.05, 8.1, 8.0, 8.0, 8.0, 8.05, 8.05, 8.1], [8.05, 8.1, 8.0, 8.0, 8.0, 8.05, 8.05, 8.1], [8.05, 8.1, 8.0, 8.0, 8.0, 8.05, 8.05, 8.1], [8.05, 8.1, 8.0, 8.0, 8.0, 8.05, 8.05, 8.1], [8.05, 8.15, 8.0, 8.0, 8.05, 8.05, 8.05, 8.1], [8.1, 8.2, 8.0, 8.1, 8.05, 8.1, 8.05, 8.1], [8.1, 8.25, 8.0, 8.1, 8.05, 8.1, 8.1, 8.1], [8.1, 8.25, 8.05, 8.1, 8.1, 8.1, 8.2, 8.1], [8.2, 8.3, 8.15, 8.15, 8.1, 8.2, 8.3, 8.1], [8.25, 8.3, 8.3, 8.2, 8.1, 8.2, 8.3, 8.1], [8.3, 8.5, 8.4, 8.25, 8.1, 8.25, 8.3, 8.1], [8.3, 8.55, 8.45, 8.25, 8.2, 8.35, 8.3, 8.1], [8.25, 8.55, 8.7, 8.4, 8.3, 8.35, 8.3, 8.1], [8.25, 8.55, 8.7, 8.4, 8.4, 8.5, 8.3, 8.25], [8.45, 8.55, 8.7, 8.45, 8.65, 8.75, 8.3, 8.55], [8.7, 8.6, 8.7, 8.45, 8.8, 8.8, 8.4, 8.7], [8.9, 8.8, 8.7, 8.6, 8.75, 8.85, 8.7, 8.85], [8.95, 9.0, 8.85, 8.75, 8.95, 9.2, 8.85, 9.3], [9.05, 9.05, 9.15, 9.15, 9.0, 9.4, 8.95, 9.4], [9.15, 9.15, 9.45, 9.3, 9.4, 9.5, 9.35, 9.55], [9.35, 9.65, 9.55, 9.5, 9.75, 9.55, 9.6, 9.9], [9.75, 9.95, 10.15, 9.95, 10.25, 9.7, 10.1, 10.0], [10.1, 10.4, 10.7, 10.9, 11.15, 10.65, 10.7, 10.3], [11.05, 10.85, 11.05, 11.15, 11.7, 11.15, 11.05, 10.9], [11.3, 11.7, 11.7, 12.15, 12.35, 11.5, 11.85, 12.0], [12.35, 12.55, 12.3, 12.65, 12.85, 12.25, 12.5, 12.85], [13.6, 13.6, 13.15, 13.5, 13.95, 13.3, 13.1, 13.5], [14.3, 14.7, 14.7, 14.4, 14.65, 14.55, 15.05, 14.75], [16.0, 16.0, 16.0, 16.0, 16.0, 16.0, 16.0, 16.0]]}
In [24]:
experiment_4 = experiments(60, 8, 100, 8, params)
print(experiment_4)
Starting the experiments...
Starting the integration...Starting the integration...Starting the integration...Starting the integration...Starting the integration...Starting the integration...Starting the integration...Starting the integration... Computing graph 1/100... Integration finished. Linear algebra computations... Computations finished. Integration finished. Linear algebra computations... Computations finished. Integration finished. Linear algebra computations... Computations finished. Integration finished. Linear algebra computations... Computations finished. Integration finished. Linear algebra computations... Computations finished. Integration finished. Linear algebra computations... Integration finished. Computations finished.Linear algebra computations... Computations finished. Integration finished. Linear algebra computations... Computations finished. Starting the integration...Starting the integration...Starting the integration...Starting the integration... Starting the integration... Starting the integration...Starting the integration...Starting the integration... Computing graph 2/100... Integration finished. Linear algebra computations... Computations finished. Integration finished. Linear algebra computations... Computations finished. Integration finished. Linear algebra computations... Computations finished. Integration finished. Linear algebra computations... Computations finished. Integration finished.Integration finished. Linear algebra computations...Linear algebra computations... Computations finished. Computations finished. Integration finished. Linear algebra computations... Computations finished. Integration finished. Linear algebra computations... Computations finished. Starting the integration...Starting the integration... Starting the integration...Starting the integration...Starting the integration...Starting the integration...Starting the integration...Starting the integration... Computing graph 3/100... Integration finished. Linear algebra computations... Computations finished. Integration finished. Linear algebra computations... Computations finished. Integration finished. Linear algebra computations... Computations finished. Integration finished. Linear algebra computations... Computations finished. Integration finished. Integration finished.Linear algebra computations... Linear algebra computations... Computations finished.Computations finished. Integration finished. Linear algebra computations... Computations finished. Integration finished. Linear algebra computations... Computations finished. Starting the integration...Starting the integration...Starting the integration...Starting the integration... Starting the integration...Starting the integration...Starting the integration...Starting the integration... Computing graph 4/100... Integration finished. Linear algebra computations... Computations finished. Integration finished. Linear algebra computations... Computations finished. Integration finished. Linear algebra computations...Integration finished. Linear algebra computations... Computations finished.Computations finished. Integration finished.Integration finished. Linear algebra computations...Linear algebra computations... Computations finished.Computations finished. Integration finished. Linear algebra computations... Computations finished. Integration finished. Linear algebra computations... Computations finished. Starting the integration...Starting the integration... Starting the integration...Starting the integration...Starting the integration...Starting the integration...Starting the integration... Starting the integration... Computing graph 5/100... Integration finished. Linear algebra computations... Computations finished. Integration finished. Linear algebra computations... Computations finished. Integration finished. Linear algebra computations... Computations finished. Integration finished. Linear algebra computations... Computations finished. Integration finished. Linear algebra computations... Computations finished. Integration finished. Integration finished.Linear algebra computations... Linear algebra computations... Computations finished. Computations finished. Integration finished. Linear algebra computations... Computations finished. Starting the integration...Starting the integration...Starting the integration...Starting the integration...Starting the integration... Starting the integration...Starting the integration... Starting the integration... Computing graph 6/100... Integration finished. Linear algebra computations... Computations finished. Integration finished. Linear algebra computations... Computations finished. Integration finished. Linear algebra computations... Computations finished. Integration finished. Linear algebra computations... Computations finished. Integration finished. Linear algebra computations... Computations finished. Integration finished. Linear algebra computations... Computations finished. Integration finished. Linear algebra computations... Integration finished. Computations finished.Linear algebra computations... Computations finished. Starting the integration...Starting the integration...Starting the integration...Starting the integration... Starting the integration...Starting the integration...Starting the integration... Starting the integration... Computing graph 7/100... Integration finished. Linear algebra computations... Computations finished. Integration finished. Linear algebra computations... Computations finished. Integration finished. Linear algebra computations... Computations finished. Integration finished. Linear algebra computations... Computations finished. Integration finished. Linear algebra computations... Computations finished. Integration finished.Integration finished. Linear algebra computations...Linear algebra computations... Integration finished. Computations finished.Computations finished.Linear algebra computations... Computations finished. Starting the integration...Starting the integration... Starting the integration...Starting the integration...Starting the integration...Starting the integration...Starting the integration...Starting the integration... Computing graph 8/100... Integration finished. Linear algebra computations... Computations finished. Integration finished. Linear algebra computations... Computations finished. Integration finished. Linear algebra computations... Integration finished. Linear algebra computations...Computations finished. Computations finished. Integration finished. Linear algebra computations... Computations finished. Integration finished. Linear algebra computations... Computations finished. Integration finished. Linear algebra computations... Computations finished. Integration finished. Linear algebra computations... Computations finished. Starting the integration...Starting the integration...Starting the integration... Starting the integration...Starting the integration... Starting the integration...Starting the integration... Starting the integration... Computing graph 9/100... Integration finished. Linear algebra computations... Computations finished. Integration finished. Linear algebra computations... Computations finished. Integration finished. Linear algebra computations... Computations finished. Integration finished. Linear algebra computations... Computations finished. Integration finished. Linear algebra computations... Computations finished. Integration finished. Linear algebra computations... Computations finished. Integration finished. Linear algebra computations... Computations finished. Integration finished. Linear algebra computations... Computations finished. Starting the integration...Starting the integration...Starting the integration...Starting the integration... Starting the integration...Starting the integration...Starting the integration... Starting the integration... Computing graph 10/100... Integration finished. Linear algebra computations... Computations finished. Integration finished. Linear algebra computations... Computations finished. Integration finished. Linear algebra computations... Computations finished. Integration finished. Linear algebra computations... Computations finished. Integration finished. Linear algebra computations... Computations finished. Integration finished. Integration finished.Linear algebra computations... Linear algebra computations... Computations finished. Computations finished. Integration finished. Linear algebra computations... Computations finished. Starting the integration...Starting the integration...Starting the integration...Starting the integration... Starting the integration...Starting the integration... Starting the integration... Starting the integration... Computing graph 11/100... Integration finished. Linear algebra computations... Computations finished. Integration finished. Linear algebra computations... Computations finished. Integration finished. Linear algebra computations... Computations finished. Integration finished. Linear algebra computations... Integration finished. Computations finished.Linear algebra computations... Computations finished. Integration finished. Linear algebra computations... Integration finished. Linear algebra computations...Computations finished. Computations finished. Integration finished. Linear algebra computations... Computations finished. Starting the integration...Starting the integration... Starting the integration... Starting the integration...Starting the integration...Starting the integration... Starting the integration... Computing graph 12/100... Starting the integration... Integration finished. Linear algebra computations... Computations finished. Integration finished. Integration finished.Linear algebra computations... Linear algebra computations... Computations finished. Computations finished. Integration finished. Linear algebra computations... Computations finished. Integration finished. Integration finished.Linear algebra computations... Linear algebra computations...Integration finished. Computations finished.Linear algebra computations...Computations finished. Computations finished. Integration finished. Linear algebra computations... Computations finished. Starting the integration...Starting the integration... Starting the integration... Starting the integration...Starting the integration... Starting the integration...Starting the integration... Starting the integration... Computing graph 13/100... Integration finished. Linear algebra computations... Computations finished. Integration finished. Linear algebra computations... Computations finished. Integration finished. Linear algebra computations... Computations finished. Integration finished. Linear algebra computations... Computations finished. Integration finished. Linear algebra computations... Computations finished. Integration finished. Linear algebra computations... Computations finished. Integration finished. Linear algebra computations... Computations finished. Integration finished. Linear algebra computations... Computations finished. Starting the integration...Starting the integration... Starting the integration... Starting the integration... Computing graph 14/100... Starting the integration... Starting the integration... Starting the integration... Starting the integration... Integration finished. Linear algebra computations... Computations finished. Integration finished. Linear algebra computations... Computations finished. Integration finished.Integration finished. Linear algebra computations... Linear algebra computations... Computations finished. Computations finished. Integration finished.Integration finished. Linear algebra computations...Linear algebra computations... Computations finished. Computations finished. Integration finished. Linear algebra computations... Computations finished. Integration finished. Linear algebra computations... Computations finished. Starting the integration...Starting the integration... Starting the integration...Starting the integration...Starting the integration... Computing graph 15/100... Starting the integration... Starting the integration... Starting the integration... Integration finished. Linear algebra computations... Computations finished. Integration finished. Linear algebra computations... Computations finished. Integration finished.Integration finished. Linear algebra computations...Linear algebra computations... Computations finished.Computations finished. Integration finished. Linear algebra computations... Computations finished. Integration finished.Integration finished. Linear algebra computations...Linear algebra computations... Computations finished.Computations finished. Integration finished. Linear algebra computations... Computations finished. Starting the integration...Starting the integration...Starting the integration...Starting the integration...Starting the integration... Starting the integration... Computing graph 16/100... Starting the integration... Starting the integration... Integration finished. Linear algebra computations... Computations finished. Integration finished. Linear algebra computations... Computations finished. Integration finished. Linear algebra computations... Computations finished. Integration finished. Linear algebra computations... Computations finished. Integration finished. Linear algebra computations... Computations finished. Integration finished. Linear algebra computations... Computations finished. Integration finished. Linear algebra computations... Computations finished. Integration finished. Linear algebra computations... Computations finished. Starting the integration... Starting the integration...Starting the integration...Starting the integration...Starting the integration...Starting the integration... Starting the integration... Computing graph 17/100... Starting the integration... Integration finished. Linear algebra computations... Computations finished. Integration finished. Linear algebra computations... Computations finished. Integration finished. Linear algebra computations... Computations finished. Integration finished. Linear algebra computations... Computations finished.Integration finished. Linear algebra computations... Computations finished. Integration finished. Linear algebra computations... Computations finished. Integration finished. Linear algebra computations... Computations finished. Integration finished. Linear algebra computations... Computations finished. Starting the integration...Starting the integration...Starting the integration...Starting the integration... Starting the integration...Starting the integration...Starting the integration... Starting the integration... Computing graph 18/100... Integration finished. Linear algebra computations... Computations finished. Integration finished. Linear algebra computations... Computations finished. Integration finished. Linear algebra computations... Computations finished. Integration finished. Linear algebra computations... Computations finished. Integration finished. Linear algebra computations... Computations finished. Integration finished. Linear algebra computations... Computations finished. Integration finished. Linear algebra computations... Computations finished. Integration finished. Linear algebra computations... Computations finished. Starting the integration...Starting the integration...Starting the integration... Starting the integration... Starting the integration...Starting the integration... Starting the integration...Starting the integration... Computing graph 19/100... Integration finished. Linear algebra computations... Computations finished. Integration finished. Linear algebra computations... Computations finished. Integration finished. Linear algebra computations... Computations finished. Integration finished. Linear algebra computations... Computations finished. Integration finished. Linear algebra computations... Computations finished. Integration finished. Linear algebra computations... Computations finished. Integration finished. Linear algebra computations... Computations finished. Integration finished. Linear algebra computations... Computations finished. Starting the integration...Starting the integration...Starting the integration...Starting the integration...Starting the integration...Starting the integration... Starting the integration...Starting the integration... Computing graph 20/100... Integration finished. Linear algebra computations... Integration finished. Computations finished.Linear algebra computations... Computations finished. Integration finished. Linear algebra computations... Computations finished. Integration finished. Linear algebra computations... Computations finished. Integration finished. Linear algebra computations... Computations finished. Integration finished. Linear algebra computations... Computations finished. Integration finished. Linear algebra computations...Integration finished. Linear algebra computations... Computations finished. Computations finished. Starting the integration...Starting the integration...Starting the integration... Starting the integration...Starting the integration...Starting the integration...Starting the integration... Starting the integration... Computing graph 21/100... Integration finished. Linear algebra computations... Computations finished. Integration finished. Linear algebra computations... Computations finished. Integration finished. Linear algebra computations... Computations finished. Integration finished. Linear algebra computations... Computations finished. Integration finished. Linear algebra computations... Integration finished. Computations finished.Linear algebra computations... Computations finished. Integration finished.Integration finished. Linear algebra computations... Linear algebra computations... Computations finished. Computations finished. Starting the integration...Starting the integration...Starting the integration...Starting the integration... Starting the integration...Starting the integration...Starting the integration...Starting the integration... Computing graph 22/100... Integration finished. Linear algebra computations... Computations finished. Integration finished. Linear algebra computations... Computations finished. Integration finished. Linear algebra computations... Computations finished. Integration finished. Linear algebra computations... Computations finished. Integration finished. Linear algebra computations... Computations finished. Integration finished. Linear algebra computations... Computations finished. Integration finished. Linear algebra computations... Computations finished. Integration finished. Linear algebra computations... Computations finished. Starting the integration...Starting the integration...Starting the integration...Starting the integration...Starting the integration...Starting the integration...Starting the integration... Starting the integration... Computing graph 23/100... Integration finished. Linear algebra computations... Computations finished. Integration finished. Linear algebra computations... Computations finished. Integration finished. Linear algebra computations... Computations finished. Integration finished. Linear algebra computations... Integration finished.Computations finished. Linear algebra computations... Computations finished. Integration finished. Linear algebra computations... Computations finished. Integration finished. Linear algebra computations... Computations finished. Integration finished. Linear algebra computations... Computations finished. Starting the integration...Starting the integration...Starting the integration...Starting the integration... Starting the integration... Starting the integration...Starting the integration...Starting the integration... Computing graph 24/100... Integration finished. Linear algebra computations... Computations finished. Integration finished. Linear algebra computations... Computations finished. Integration finished. Linear algebra computations... Computations finished. Integration finished. Linear algebra computations... Computations finished. Integration finished. Linear algebra computations... Computations finished. Integration finished. Linear algebra computations... Computations finished. Integration finished. Linear algebra computations... Computations finished. Integration finished. Linear algebra computations... Computations finished. Starting the integration...Starting the integration...Starting the integration...Starting the integration... Starting the integration...Starting the integration...Starting the integration... Starting the integration... Computing graph 25/100... Integration finished. Linear algebra computations... Computations finished. Integration finished. Linear algebra computations... Computations finished. Integration finished. Linear algebra computations... Computations finished. Integration finished. Linear algebra computations... Computations finished. Integration finished. Linear algebra computations... Computations finished. Integration finished. Linear algebra computations... Computations finished. Integration finished. Linear algebra computations... Computations finished. Integration finished. Linear algebra computations... Computations finished. Starting the integration...Starting the integration...Starting the integration...Starting the integration...Starting the integration...Starting the integration...Starting the integration... Starting the integration... Computing graph 26/100... Integration finished. Linear algebra computations... Computations finished. Integration finished. Linear algebra computations... Computations finished. Integration finished. Linear algebra computations... Computations finished. Integration finished. Linear algebra computations... Computations finished. Integration finished. Linear algebra computations... Computations finished. Integration finished. Linear algebra computations... Integration finished. Computations finished.Linear algebra computations... Computations finished. Integration finished. Linear algebra computations... Computations finished. Starting the integration...Starting the integration...Starting the integration...Starting the integration... Starting the integration...Starting the integration...Starting the integration... Starting the integration... Computing graph 27/100... Integration finished. Linear algebra computations... Computations finished. Integration finished. Linear algebra computations... Computations finished. Integration finished. Linear algebra computations... Computations finished. Integration finished. Linear algebra computations... Computations finished. Integration finished. Linear algebra computations... Computations finished. Integration finished. Linear algebra computations... Computations finished. Integration finished. Linear algebra computations... Computations finished. Integration finished. Linear algebra computations... Computations finished. Starting the integration...Starting the integration...Starting the integration...Starting the integration...Starting the integration... Starting the integration...Starting the integration... Starting the integration... Computing graph 28/100... Integration finished. Linear algebra computations... Computations finished. Integration finished. Linear algebra computations... Computations finished. Integration finished. Linear algebra computations... Computations finished. Integration finished. Linear algebra computations... Integration finished. Computations finished.Linear algebra computations... Computations finished. Integration finished. Linear algebra computations...Integration finished. Linear algebra computations... Computations finished. Computations finished. Integration finished. Linear algebra computations... Computations finished. Starting the integration...Starting the integration...Starting the integration...Starting the integration... Starting the integration...Starting the integration...Starting the integration...Starting the integration... Computing graph 29/100... Integration finished. Linear algebra computations... Computations finished. Integration finished. Linear algebra computations... Computations finished.Integration finished. Linear algebra computations... Computations finished. Integration finished. Linear algebra computations... Computations finished. Integration finished. Linear algebra computations... Computations finished. Integration finished. Linear algebra computations... Computations finished. Integration finished. Linear algebra computations... Computations finished. Integration finished. Linear algebra computations... Computations finished. Starting the integration...Starting the integration... Starting the integration...Starting the integration...Starting the integration...Starting the integration... Starting the integration... Starting the integration... Computing graph 30/100... Integration finished. Linear algebra computations... Computations finished. Integration finished. Linear algebra computations... Computations finished. Integration finished. Linear algebra computations... Integration finished. Linear algebra computations...Computations finished. Integration finished. Computations finished.Linear algebra computations... Computations finished. Integration finished. Linear algebra computations... Computations finished. Integration finished. Linear algebra computations... Computations finished. Integration finished. Linear algebra computations... Computations finished. Starting the integration...Starting the integration...Starting the integration...Starting the integration...Starting the integration...Starting the integration...Starting the integration... Starting the integration... Computing graph 31/100... Integration finished. Linear algebra computations... Computations finished. Integration finished. Linear algebra computations... Computations finished. Integration finished. Linear algebra computations... Computations finished. Integration finished. Linear algebra computations... Integration finished.Computations finished. Linear algebra computations... Computations finished. Integration finished. Linear algebra computations... Computations finished. Integration finished. Linear algebra computations... Computations finished. Integration finished. Linear algebra computations... Computations finished. Starting the integration...Starting the integration...Starting the integration... Starting the integration...Starting the integration...Starting the integration...Starting the integration... Starting the integration... Computing graph 32/100... Integration finished. Linear algebra computations... Computations finished. Integration finished. Linear algebra computations... Computations finished. Integration finished. Linear algebra computations... Computations finished. Integration finished. Linear algebra computations... Computations finished. Integration finished. Linear algebra computations... Computations finished. Integration finished. Linear algebra computations... Computations finished. Integration finished. Linear algebra computations... Computations finished. Integration finished. Linear algebra computations... Computations finished. Starting the integration...Starting the integration...Starting the integration...Starting the integration... Starting the integration...Starting the integration... Starting the integration... Starting the integration... Computing graph 33/100... Integration finished. Linear algebra computations...Integration finished. Linear algebra computations...Computations finished. Computations finished. Integration finished. Linear algebra computations... Computations finished. Integration finished. Linear algebra computations... Computations finished. Integration finished. Linear algebra computations... Computations finished. Integration finished. Linear algebra computations... Computations finished. Integration finished.Integration finished. Linear algebra computations...Linear algebra computations... Computations finished.Computations finished. Starting the integration...Starting the integration...Starting the integration... Starting the integration...Starting the integration... Starting the integration...Starting the integration...Starting the integration... Computing graph 34/100... Integration finished. Linear algebra computations... Computations finished. Integration finished. Linear algebra computations... Computations finished. Integration finished. Linear algebra computations... Computations finished. Integration finished. Linear algebra computations... Computations finished. Integration finished. Linear algebra computations... Computations finished. Integration finished. Linear algebra computations... Computations finished. Integration finished. Linear algebra computations... Computations finished. Integration finished. Linear algebra computations... Computations finished. Starting the integration...Starting the integration...Starting the integration...Starting the integration... Starting the integration...Starting the integration...Starting the integration...Starting the integration... Computing graph 35/100... Integration finished. Linear algebra computations... Computations finished. Integration finished. Linear algebra computations... Computations finished. Integration finished. Linear algebra computations... Computations finished. Integration finished. Linear algebra computations... Computations finished. Integration finished.Integration finished. Linear algebra computations...Integration finished.Linear algebra computations... Linear algebra computations... Computations finished.Computations finished. Computations finished. Integration finished. Linear algebra computations... Computations finished. Starting the integration...Starting the integration...Starting the integration...Starting the integration... Starting the integration...Starting the integration...Starting the integration... Starting the integration... Computing graph 36/100... Integration finished. Linear algebra computations... Computations finished. Integration finished. Linear algebra computations... Computations finished. Integration finished. Linear algebra computations... Computations finished. Integration finished. Linear algebra computations... Computations finished. Integration finished. Linear algebra computations... Computations finished. Integration finished. Linear algebra computations... Computations finished.Integration finished. Linear algebra computations... Computations finished. Integration finished. Linear algebra computations... Computations finished. Starting the integration...Starting the integration...Starting the integration...Starting the integration... Starting the integration...Starting the integration... Starting the integration...Starting the integration... Computing graph 37/100... Integration finished. Linear algebra computations... Computations finished. Integration finished. Linear algebra computations... Computations finished. Integration finished. Integration finished.Linear algebra computations... Linear algebra computations... Computations finished. Computations finished. Integration finished. Linear algebra computations... Computations finished. Integration finished. Linear algebra computations... Computations finished. Integration finished. Linear algebra computations... Computations finished. Integration finished. Linear algebra computations... Computations finished. Starting the integration...Starting the integration...Starting the integration...Starting the integration... Starting the integration...Starting the integration...Starting the integration... Starting the integration... Computing graph 38/100... Integration finished. Linear algebra computations... Computations finished. Integration finished. Linear algebra computations... Computations finished. Integration finished. Linear algebra computations... Computations finished. Integration finished. Linear algebra computations... Computations finished. Integration finished. Linear algebra computations... Computations finished. Integration finished. Linear algebra computations... Computations finished. Integration finished. Linear algebra computations... Computations finished. Integration finished. Linear algebra computations... Computations finished. Starting the integration...Starting the integration...Starting the integration...Starting the integration...Starting the integration...Starting the integration... Starting the integration...Starting the integration... Computing graph 39/100... Integration finished. Linear algebra computations... Computations finished. Integration finished. Linear algebra computations... Integration finished. Computations finished.Linear algebra computations... Computations finished. Integration finished. Linear algebra computations... Computations finished. Integration finished. Linear algebra computations... Computations finished. Integration finished. Linear algebra computations... Integration finished. Computations finished.Linear algebra computations... Integration finished.Computations finished. Linear algebra computations...
/tmp/ipykernel_55793/633668650.py:161: ComplexWarning: Casting complex values to real discards the imaginary part 'critical_eigenvalue': float(eigenvalues[index_lambda_c]), /tmp/ipykernel_55793/633668650.py:171: ComplexWarning: Casting complex values to real discards the imaginary part 'ipr_eigenvector': float(ipr_eigenvector),
Computations finished. Starting the integration...Starting the integration...Starting the integration... Starting the integration...Starting the integration... Starting the integration...Starting the integration... Starting the integration... Computing graph 40/100... Integration finished. Linear algebra computations... Computations finished. Integration finished. Linear algebra computations... Computations finished. Integration finished. Linear algebra computations... Integration finished. Computations finished.Linear algebra computations... Computations finished. Integration finished. Linear algebra computations... Computations finished.
/tmp/ipykernel_55793/633668650.py:161: ComplexWarning: Casting complex values to real discards the imaginary part 'critical_eigenvalue': float(eigenvalues[index_lambda_c]), /tmp/ipykernel_55793/633668650.py:171: ComplexWarning: Casting complex values to real discards the imaginary part 'ipr_eigenvector': float(ipr_eigenvector),
Integration finished. Linear algebra computations... Computations finished. Integration finished. Linear algebra computations... Computations finished. Integration finished. Linear algebra computations... Computations finished. Starting the integration...Starting the integration...Starting the integration...Starting the integration... Starting the integration...Starting the integration... Starting the integration...Starting the integration... Computing graph 41/100... Integration finished. Linear algebra computations... Computations finished. Integration finished. Linear algebra computations... Integration finished.Computations finished. Linear algebra computations... Computations finished. Integration finished. Linear algebra computations... Computations finished. Integration finished. Linear algebra computations... Computations finished.
/tmp/ipykernel_55793/633668650.py:161: ComplexWarning: Casting complex values to real discards the imaginary part 'critical_eigenvalue': float(eigenvalues[index_lambda_c]), /tmp/ipykernel_55793/633668650.py:171: ComplexWarning: Casting complex values to real discards the imaginary part 'ipr_eigenvector': float(ipr_eigenvector),
Integration finished. Linear algebra computations... Integration finished.Computations finished. Linear algebra computations... Integration finished. Computations finished.Linear algebra computations... Computations finished. Starting the integration...Starting the integration...Starting the integration... Starting the integration...Starting the integration... Starting the integration... Starting the integration... Starting the integration... Computing graph 42/100... Integration finished. Linear algebra computations... Computations finished. Integration finished. Linear algebra computations... Computations finished. Integration finished. Linear algebra computations... Computations finished. Integration finished.Integration finished. Linear algebra computations...Linear algebra computations... Computations finished. Computations finished. Integration finished. Linear algebra computations... Computations finished. Integration finished. Linear algebra computations... Integration finished. Computations finished.Linear algebra computations...
/tmp/ipykernel_55793/633668650.py:161: ComplexWarning: Casting complex values to real discards the imaginary part 'critical_eigenvalue': float(eigenvalues[index_lambda_c]), /tmp/ipykernel_55793/633668650.py:171: ComplexWarning: Casting complex values to real discards the imaginary part 'ipr_eigenvector': float(ipr_eigenvector),
Computations finished. Starting the integration...Starting the integration...Starting the integration...Starting the integration...Starting the integration...Starting the integration...Starting the integration... Starting the integration... Computing graph 43/100... Integration finished. Linear algebra computations... Computations finished. Integration finished. Linear algebra computations... Computations finished. Integration finished. Linear algebra computations... Computations finished. Integration finished. Linear algebra computations... Computations finished. Integration finished. Linear algebra computations... Integration finished. Computations finished.Linear algebra computations... Computations finished. Integration finished. Linear algebra computations... Computations finished. Integration finished. Linear algebra computations... Computations finished. Starting the integration...Starting the integration...Starting the integration...Starting the integration... Starting the integration...Starting the integration...Starting the integration...Starting the integration... Computing graph 44/100... Integration finished. Linear algebra computations... Computations finished. Integration finished. Linear algebra computations... Computations finished. Integration finished. Linear algebra computations... Computations finished. Integration finished. Linear algebra computations... Computations finished. Integration finished. Linear algebra computations... Computations finished. Integration finished. Linear algebra computations... Computations finished. Integration finished. Linear algebra computations... Computations finished.Integration finished. Linear algebra computations... Computations finished. Starting the integration...Starting the integration... Starting the integration...Starting the integration...Starting the integration...Starting the integration... Starting the integration...Starting the integration... Computing graph 45/100... Integration finished. Linear algebra computations... Computations finished. Integration finished. Linear algebra computations... Computations finished. Integration finished. Linear algebra computations... Computations finished.Integration finished. Linear algebra computations... Computations finished. Integration finished. Linear algebra computations... Integration finished.Integration finished. Computations finished.Linear algebra computations... Linear algebra computations... Computations finished. Computations finished. Integration finished. Linear algebra computations... Computations finished. Starting the integration...Starting the integration...Starting the integration... Starting the integration...Starting the integration...Starting the integration... Starting the integration... Starting the integration... Computing graph 46/100... Integration finished. Linear algebra computations... Computations finished. Integration finished. Linear algebra computations... Computations finished. Integration finished. Linear algebra computations... Computations finished. Integration finished. Linear algebra computations... Integration finished. Computations finished.Linear algebra computations... Computations finished. Integration finished. Linear algebra computations... Computations finished. Integration finished. Linear algebra computations... Computations finished. Integration finished. Linear algebra computations... Computations finished. Starting the integration...Starting the integration...Starting the integration...Starting the integration...Starting the integration...Starting the integration...Starting the integration...Starting the integration... Computing graph 47/100... Integration finished. Linear algebra computations... Computations finished. Integration finished. Linear algebra computations... Computations finished. Integration finished. Linear algebra computations... Computations finished. Integration finished. Linear algebra computations... Computations finished. Integration finished. Linear algebra computations... Computations finished. Integration finished. Linear algebra computations... Computations finished. Integration finished. Linear algebra computations... Computations finished.Integration finished. Linear algebra computations... Computations finished. Starting the integration...Starting the integration...Starting the integration... Starting the integration... Starting the integration...Starting the integration...Starting the integration...Starting the integration... Computing graph 48/100... Integration finished. Linear algebra computations... Computations finished. Integration finished. Linear algebra computations... Computations finished. Integration finished. Linear algebra computations... Computations finished. Integration finished. Linear algebra computations... Computations finished. Integration finished. Linear algebra computations... Computations finished. Integration finished. Linear algebra computations... Computations finished. Integration finished. Linear algebra computations... Computations finished. Integration finished. Linear algebra computations... Computations finished. Starting the integration...Starting the integration...Starting the integration...Starting the integration... Starting the integration... Starting the integration... Starting the integration...Starting the integration... Computing graph 49/100... Integration finished. Linear algebra computations... Computations finished. Integration finished. Linear algebra computations... Computations finished. Integration finished. Linear algebra computations... Computations finished. Integration finished. Linear algebra computations... Computations finished. Integration finished. Linear algebra computations... Computations finished. Integration finished. Linear algebra computations... Computations finished. Integration finished. Linear algebra computations... Computations finished. Integration finished. Linear algebra computations... Computations finished. Starting the integration...Starting the integration...Starting the integration...Starting the integration... Starting the integration...Starting the integration...Starting the integration... Starting the integration... Computing graph 50/100... Integration finished. Linear algebra computations... Computations finished. Integration finished. Linear algebra computations... Computations finished. Integration finished. Linear algebra computations... Computations finished. Integration finished. Linear algebra computations... Computations finished. Integration finished. Linear algebra computations... Computations finished. Integration finished. Linear algebra computations... Computations finished. Integration finished. Linear algebra computations... Computations finished. Integration finished. Linear algebra computations... Computations finished. Starting the integration...Starting the integration...Starting the integration... Starting the integration...Starting the integration... Starting the integration...Starting the integration... Starting the integration... Computing graph 51/100... Integration finished. Linear algebra computations... Computations finished. Integration finished. Linear algebra computations... Computations finished. Integration finished. Linear algebra computations... Computations finished. Integration finished. Linear algebra computations... Computations finished. Integration finished. Linear algebra computations... Computations finished. Integration finished. Linear algebra computations... Computations finished. Integration finished. Linear algebra computations... Computations finished. Integration finished. Linear algebra computations... Computations finished. Starting the integration...Starting the integration...Starting the integration...Starting the integration...Starting the integration...Starting the integration...Starting the integration... Starting the integration... Computing graph 52/100... Integration finished. Linear algebra computations... Computations finished. Integration finished. Linear algebra computations... Computations finished. Integration finished. Linear algebra computations... Computations finished. Integration finished. Linear algebra computations... Computations finished. Integration finished. Linear algebra computations... Computations finished.Integration finished. Linear algebra computations... Computations finished. Integration finished. Linear algebra computations... Computations finished. Integration finished. Linear algebra computations... Computations finished. Starting the integration...Starting the integration...Starting the integration...Starting the integration... Starting the integration... Starting the integration... Starting the integration... Starting the integration... Computing graph 53/100... Integration finished. Linear algebra computations... Computations finished. Integration finished. Linear algebra computations... Computations finished. Integration finished. Linear algebra computations... Computations finished. Integration finished. Linear algebra computations... Computations finished. Integration finished. Linear algebra computations... Computations finished. Integration finished. Linear algebra computations... Computations finished. Integration finished. Linear algebra computations... Computations finished. Integration finished. Linear algebra computations... Computations finished. Starting the integration...Starting the integration...Starting the integration...Starting the integration... Starting the integration... Starting the integration...Starting the integration...Starting the integration... Computing graph 54/100... Integration finished. Linear algebra computations... Computations finished. Integration finished. Linear algebra computations... Computations finished. Integration finished. Linear algebra computations... Computations finished. Integration finished. Linear algebra computations... Computations finished. Integration finished. Linear algebra computations... Computations finished. Integration finished. Linear algebra computations... Computations finished. Integration finished. Linear algebra computations... Computations finished. Integration finished. Linear algebra computations... Computations finished. Starting the integration...Starting the integration... Starting the integration...Starting the integration... Starting the integration... Starting the integration...Starting the integration...Starting the integration... Computing graph 55/100... Integration finished. Linear algebra computations... Computations finished. Integration finished. Linear algebra computations... Computations finished. Integration finished. Linear algebra computations... Computations finished. Integration finished. Linear algebra computations... Computations finished. Integration finished. Linear algebra computations... Computations finished. Integration finished. Linear algebra computations... Integration finished.Computations finished. Linear algebra computations... Computations finished. Integration finished. Linear algebra computations... Computations finished. Starting the integration...Starting the integration...Starting the integration...Starting the integration... Starting the integration...Starting the integration...Starting the integration... Starting the integration... Computing graph 56/100... Integration finished. Linear algebra computations... Computations finished. Integration finished. Linear algebra computations... Computations finished. Integration finished. Linear algebra computations... Computations finished. Integration finished. Linear algebra computations... Computations finished. Integration finished. Linear algebra computations...Integration finished. Linear algebra computations... Computations finished. Computations finished. Integration finished. Linear algebra computations... Computations finished. Integration finished. Linear algebra computations... Computations finished. Starting the integration...Starting the integration...Starting the integration...Starting the integration... Starting the integration...Starting the integration... Starting the integration... Starting the integration... Computing graph 57/100... Integration finished. Linear algebra computations... Computations finished. Integration finished. Linear algebra computations... Computations finished. Integration finished. Linear algebra computations... Computations finished. Integration finished. Linear algebra computations... Computations finished. Integration finished. Linear algebra computations... Computations finished. Integration finished. Linear algebra computations... Integration finished. Linear algebra computations...Computations finished. Computations finished. Integration finished. Linear algebra computations... Computations finished. Starting the integration... Starting the integration...Starting the integration... Starting the integration... Starting the integration...Starting the integration... Starting the integration...Starting the integration... Computing graph 58/100... Integration finished. Linear algebra computations... Computations finished.
/tmp/ipykernel_55793/633668650.py:161: ComplexWarning: Casting complex values to real discards the imaginary part 'critical_eigenvalue': float(eigenvalues[index_lambda_c]), /tmp/ipykernel_55793/633668650.py:171: ComplexWarning: Casting complex values to real discards the imaginary part 'ipr_eigenvector': float(ipr_eigenvector),
Integration finished. Linear algebra computations... Computations finished. Integration finished. Linear algebra computations... Computations finished. Integration finished. Linear algebra computations... Computations finished. Integration finished. Linear algebra computations... Computations finished. Integration finished. Linear algebra computations... Computations finished. Integration finished. Linear algebra computations... Computations finished. Integration finished. Linear algebra computations... Computations finished. Starting the integration...Starting the integration...Starting the integration... Starting the integration...Starting the integration...Starting the integration... Starting the integration... Starting the integration... Computing graph 59/100... Integration finished. Linear algebra computations... Computations finished. Integration finished. Linear algebra computations... Computations finished. Integration finished. Linear algebra computations... Computations finished. Integration finished. Linear algebra computations... Computations finished. Integration finished. Linear algebra computations... Computations finished. Integration finished. Linear algebra computations... Computations finished. Integration finished. Linear algebra computations... Computations finished. Integration finished. Linear algebra computations... Computations finished. Starting the integration...Starting the integration... Starting the integration...Starting the integration... Starting the integration...Starting the integration... Starting the integration... Starting the integration... Computing graph 60/100... Integration finished. Linear algebra computations... Computations finished. Integration finished. Linear algebra computations... Computations finished. Integration finished. Linear algebra computations... Computations finished. Integration finished. Linear algebra computations...Integration finished. Linear algebra computations... Computations finished. Computations finished. Integration finished. Linear algebra computations... Computations finished. Integration finished. Linear algebra computations... Computations finished. Integration finished. Linear algebra computations... Computations finished. Starting the integration...Starting the integration...Starting the integration...Starting the integration...Starting the integration...Starting the integration... Starting the integration... Starting the integration... Computing graph 61/100... Integration finished. Linear algebra computations... Computations finished. Integration finished. Linear algebra computations... Computations finished. Integration finished. Linear algebra computations... Computations finished. Integration finished.Integration finished. Linear algebra computations... Linear algebra computations... Integration finished.Computations finished. Computations finished.Linear algebra computations... Computations finished. Integration finished. Linear algebra computations... Integration finished. Linear algebra computations... Computations finished. Computations finished. Starting the integration...Starting the integration...Starting the integration...Starting the integration...Starting the integration...Starting the integration...Starting the integration... Starting the integration... Computing graph 62/100... Integration finished. Linear algebra computations... Computations finished. Integration finished. Linear algebra computations... Computations finished. Integration finished. Linear algebra computations... Computations finished. Integration finished. Linear algebra computations... Computations finished. Integration finished. Linear algebra computations... Computations finished. Integration finished. Linear algebra computations... Computations finished.Integration finished. Linear algebra computations... Computations finished. Integration finished. Linear algebra computations... Computations finished. Starting the integration...Starting the integration...Starting the integration...Starting the integration...Starting the integration...Starting the integration... Starting the integration...Starting the integration... Computing graph 63/100... Integration finished. Linear algebra computations... Computations finished. Integration finished. Linear algebra computations... Computations finished. Integration finished. Linear algebra computations... Computations finished. Integration finished. Linear algebra computations... Computations finished. Integration finished. Linear algebra computations... Computations finished. Integration finished. Linear algebra computations... Integration finished. Computations finished.Linear algebra computations... Computations finished. Integration finished. Linear algebra computations... Computations finished. Starting the integration...Starting the integration...Starting the integration...Starting the integration...Starting the integration... Starting the integration...Starting the integration... Starting the integration... Computing graph 64/100... Integration finished. Linear algebra computations... Computations finished. Integration finished. Linear algebra computations... Computations finished. Integration finished. Linear algebra computations... Computations finished. Integration finished. Linear algebra computations... Computations finished. Integration finished. Linear algebra computations... Computations finished. Integration finished. Linear algebra computations... Computations finished. Integration finished. Linear algebra computations... Computations finished. Integration finished. Linear algebra computations... Computations finished. Starting the integration...Starting the integration...Starting the integration...Starting the integration...Starting the integration...Starting the integration...Starting the integration... Starting the integration... Computing graph 65/100... Integration finished. Linear algebra computations... Computations finished. Integration finished. Linear algebra computations... Computations finished. Integration finished. Linear algebra computations... Computations finished. Integration finished. Linear algebra computations... Computations finished. Integration finished. Linear algebra computations... Computations finished. Integration finished. Linear algebra computations... Computations finished. Integration finished. Linear algebra computations... Computations finished. Integration finished. Linear algebra computations... Computations finished. Starting the integration...Starting the integration...Starting the integration...Starting the integration...Starting the integration...Starting the integration...Starting the integration...Starting the integration... Computing graph 66/100... Integration finished. Linear algebra computations... Computations finished. Integration finished. Linear algebra computations... Computations finished. Integration finished. Linear algebra computations... Computations finished. Integration finished. Integration finished.Linear algebra computations... Linear algebra computations... Computations finished.Computations finished. Integration finished. Linear algebra computations... Computations finished. Integration finished. Linear algebra computations... Computations finished. Integration finished. Linear algebra computations... Computations finished. Starting the integration...Starting the integration...Starting the integration...Starting the integration...Starting the integration...Starting the integration...Starting the integration... Starting the integration... Computing graph 67/100... Integration finished. Linear algebra computations... Computations finished. Integration finished. Linear algebra computations... Computations finished. Integration finished. Linear algebra computations... Computations finished. Integration finished. Linear algebra computations... Computations finished. Integration finished. Linear algebra computations... Computations finished. Integration finished. Linear algebra computations...Integration finished. Linear algebra computations... Computations finished. Computations finished. Integration finished. Linear algebra computations... Computations finished. Starting the integration...Starting the integration...Starting the integration...Starting the integration...Starting the integration... Starting the integration...Starting the integration... Starting the integration... Computing graph 68/100... Integration finished. Linear algebra computations... Computations finished. Integration finished. Linear algebra computations... Computations finished. Integration finished. Linear algebra computations... Computations finished. Integration finished. Linear algebra computations... Computations finished. Integration finished. Linear algebra computations... Computations finished. Integration finished.Integration finished. Linear algebra computations...Linear algebra computations... Computations finished.Computations finished. Integration finished. Linear algebra computations... Computations finished. Starting the integration...Starting the integration...Starting the integration... Starting the integration... Starting the integration...Starting the integration...Starting the integration... Starting the integration... Computing graph 69/100... Integration finished. Linear algebra computations... Computations finished. Integration finished. Linear algebra computations... Computations finished. Integration finished. Linear algebra computations... Computations finished. Integration finished. Linear algebra computations... Computations finished. Integration finished. Linear algebra computations... Computations finished. Integration finished. Linear algebra computations... Computations finished. Integration finished. Linear algebra computations... Computations finished. Integration finished. Linear algebra computations... Computations finished. Starting the integration...Starting the integration...Starting the integration...Starting the integration... Starting the integration... Starting the integration...Starting the integration... Starting the integration... Computing graph 70/100... Integration finished. Linear algebra computations... Computations finished. Integration finished. Linear algebra computations... Computations finished. Integration finished. Linear algebra computations... Computations finished. Integration finished. Linear algebra computations... Computations finished. Integration finished. Linear algebra computations... Computations finished. Integration finished. Linear algebra computations... Computations finished. Integration finished. Linear algebra computations... Computations finished. Integration finished. Linear algebra computations... Computations finished. Starting the integration...Starting the integration...Starting the integration...Starting the integration... Starting the integration...Starting the integration... Starting the integration... Starting the integration... Computing graph 71/100... Integration finished. Linear algebra computations... Computations finished. Integration finished. Linear algebra computations... Computations finished. Integration finished. Linear algebra computations... Computations finished. Integration finished. Linear algebra computations... Computations finished. Integration finished. Linear algebra computations... Computations finished. Integration finished. Linear algebra computations... Computations finished. Integration finished. Linear algebra computations... Computations finished. Integration finished. Linear algebra computations... Computations finished. Starting the integration...Starting the integration...Starting the integration...Starting the integration... Starting the integration...Starting the integration...Starting the integration... Starting the integration... Computing graph 72/100... Integration finished. Linear algebra computations... Computations finished. Integration finished. Linear algebra computations... Computations finished. Integration finished. Linear algebra computations... Computations finished. Integration finished. Linear algebra computations... Computations finished. Integration finished. Linear algebra computations... Computations finished. Integration finished. Linear algebra computations... Computations finished. Integration finished. Linear algebra computations... Computations finished. Integration finished. Linear algebra computations... Computations finished. Starting the integration...Starting the integration...Starting the integration...Starting the integration...Starting the integration... Starting the integration... Starting the integration...Starting the integration... Computing graph 73/100... Integration finished. Linear algebra computations... Computations finished. Integration finished. Linear algebra computations... Computations finished. Integration finished. Linear algebra computations... Computations finished. Integration finished. Linear algebra computations... Computations finished. Integration finished. Linear algebra computations... Computations finished. Integration finished. Linear algebra computations... Computations finished. Integration finished. Linear algebra computations... Computations finished. Integration finished. Linear algebra computations... Computations finished. Starting the integration...Starting the integration...Starting the integration...Starting the integration... Starting the integration...Starting the integration...Starting the integration...Starting the integration... Computing graph 74/100... Integration finished. Linear algebra computations... Computations finished. Integration finished. Linear algebra computations... Computations finished. Integration finished. Linear algebra computations... Computations finished. Integration finished. Linear algebra computations... Computations finished. Integration finished. Linear algebra computations... Computations finished. Integration finished. Linear algebra computations... Computations finished. Integration finished. Linear algebra computations... Integration finished. Linear algebra computations... Computations finished. Computations finished. Starting the integration...Starting the integration...Starting the integration...Starting the integration...Starting the integration...Starting the integration... Starting the integration... Starting the integration... Computing graph 75/100... Integration finished. Linear algebra computations... Computations finished. Integration finished. Linear algebra computations... Computations finished. Integration finished. Linear algebra computations... Computations finished. Integration finished. Linear algebra computations... Computations finished. Integration finished. Linear algebra computations... Computations finished. Integration finished. Linear algebra computations... Computations finished. Integration finished. Linear algebra computations... Computations finished. Integration finished. Linear algebra computations... Computations finished. Starting the integration...Starting the integration... Starting the integration...Starting the integration...Starting the integration...Starting the integration... Starting the integration... Starting the integration... Computing graph 76/100... Integration finished. Linear algebra computations... Computations finished. Integration finished. Integration finished.Linear algebra computations... Linear algebra computations... Computations finished. Computations finished. Integration finished. Linear algebra computations... Computations finished. Integration finished. Linear algebra computations... Computations finished. Integration finished. Linear algebra computations... Computations finished.Integration finished. Linear algebra computations... Computations finished. Integration finished. Linear algebra computations... Computations finished. Starting the integration...Starting the integration...Starting the integration... Starting the integration...Starting the integration...Starting the integration...Starting the integration... Starting the integration... Computing graph 77/100... Integration finished. Linear algebra computations... Computations finished. Integration finished. Linear algebra computations... Computations finished. Integration finished. Linear algebra computations... Computations finished. Integration finished. Linear algebra computations... Computations finished. Integration finished. Linear algebra computations... Computations finished. Integration finished. Linear algebra computations... Computations finished. Integration finished. Linear algebra computations... Computations finished. Integration finished. Linear algebra computations... Computations finished. Starting the integration...Starting the integration...Starting the integration...Starting the integration...Starting the integration...Starting the integration...Starting the integration... Starting the integration... Computing graph 78/100... Integration finished. Linear algebra computations... Computations finished. Integration finished. Linear algebra computations... Computations finished. Integration finished. Linear algebra computations... Computations finished. Integration finished. Linear algebra computations... Computations finished. Integration finished. Linear algebra computations... Integration finished. Computations finished.Linear algebra computations... Computations finished. Integration finished. Linear algebra computations... Computations finished. Integration finished. Linear algebra computations... Computations finished. Starting the integration...Starting the integration...Starting the integration...Starting the integration...Starting the integration... Starting the integration... Starting the integration... Starting the integration... Computing graph 79/100... Integration finished. Linear algebra computations... Computations finished. Integration finished. Linear algebra computations... Computations finished. Integration finished. Linear algebra computations... Computations finished. Integration finished. Linear algebra computations... Computations finished. Integration finished. Linear algebra computations... Computations finished. Integration finished. Linear algebra computations... Computations finished. Integration finished. Linear algebra computations... Computations finished. Integration finished. Linear algebra computations... Computations finished. Starting the integration...Starting the integration...Starting the integration...Starting the integration... Starting the integration... Starting the integration...Starting the integration... Starting the integration... Computing graph 80/100... Integration finished. Linear algebra computations... Computations finished. Integration finished. Linear algebra computations... Computations finished. Integration finished. Linear algebra computations... Computations finished. Integration finished. Linear algebra computations... Computations finished. Integration finished. Linear algebra computations... Computations finished. Integration finished. Linear algebra computations... Computations finished. Integration finished. Linear algebra computations... Integration finished. Computations finished.Linear algebra computations... Computations finished. Starting the integration...Starting the integration...Starting the integration...Starting the integration... Starting the integration...Starting the integration... Starting the integration...Starting the integration... Computing graph 81/100... Integration finished. Linear algebra computations... Computations finished. Integration finished. Linear algebra computations... Computations finished. Integration finished. Linear algebra computations... Computations finished. Integration finished. Linear algebra computations... Computations finished. Integration finished. Linear algebra computations... Computations finished. Integration finished. Linear algebra computations... Computations finished. Integration finished. Linear algebra computations... Computations finished. Integration finished. Linear algebra computations... Computations finished. Starting the integration...Starting the integration...Starting the integration...Starting the integration... Starting the integration...Starting the integration...Starting the integration... Starting the integration... Computing graph 82/100... Integration finished. Linear algebra computations... Computations finished. Integration finished. Linear algebra computations... Computations finished. Integration finished. Linear algebra computations... Computations finished. Integration finished. Linear algebra computations... Computations finished. Integration finished. Linear algebra computations... Computations finished. Integration finished. Linear algebra computations... Computations finished. Integration finished. Linear algebra computations... Computations finished. Integration finished. Linear algebra computations... Computations finished. Starting the integration...Starting the integration... Starting the integration...Starting the integration...Starting the integration...Starting the integration... Starting the integration... Starting the integration... Computing graph 83/100... Integration finished. Linear algebra computations... Computations finished. Integration finished. Linear algebra computations... Computations finished. Integration finished. Linear algebra computations... Computations finished. Integration finished. Linear algebra computations... Computations finished. Integration finished. Linear algebra computations... Computations finished. Integration finished. Linear algebra computations... Computations finished. Integration finished. Linear algebra computations... Computations finished. Integration finished. Linear algebra computations... Computations finished. Starting the integration...Starting the integration...Starting the integration...Starting the integration... Starting the integration... Starting the integration...Starting the integration... Starting the integration... Computing graph 84/100... Integration finished. Linear algebra computations... Computations finished. Integration finished. Linear algebra computations... Computations finished. Integration finished. Linear algebra computations... Computations finished. Integration finished. Linear algebra computations... Computations finished. Integration finished. Integration finished.Linear algebra computations... Linear algebra computations... Computations finished. Computations finished. Integration finished. Linear algebra computations... Computations finished. Integration finished. Linear algebra computations... Computations finished. Starting the integration...Starting the integration...Starting the integration... Starting the integration... Starting the integration...Starting the integration... Starting the integration...Starting the integration... Computing graph 85/100... Integration finished. Linear algebra computations... Computations finished. Integration finished. Linear algebra computations... Computations finished. Integration finished. Linear algebra computations... Computations finished. Integration finished. Linear algebra computations... Computations finished. Integration finished. Linear algebra computations... Computations finished. Integration finished.Integration finished. Linear algebra computations...Linear algebra computations... Computations finished.Computations finished. Integration finished. Linear algebra computations... Computations finished. Starting the integration... Starting the integration...Starting the integration...Starting the integration...Starting the integration...Starting the integration... Starting the integration...Starting the integration... Computing graph 86/100... Integration finished. Linear algebra computations... Computations finished. Integration finished. Linear algebra computations... The critical eigenvalue is not in the range of the dispersion relation. The linear analysis cannot be performed. The critical eigenvalue is: -2.246823104399011
/tmp/ipykernel_55793/633668650.py:148: RuntimeWarning: invalid value encountered in scalar divide ipr_eigenvector = np.sum(critical_eigenvector**4) / (np.sum(critical_eigenvector**2)**2)
Computations finished. Integration finished. Linear algebra computations... Computations finished. Integration finished. Linear algebra computations... Computations finished. Integration finished. Linear algebra computations... Computations finished. Integration finished. Linear algebra computations... Computations finished. Integration finished. Linear algebra computations... Computations finished. Integration finished. Linear algebra computations... Computations finished. Starting the integration...Starting the integration...Starting the integration...Starting the integration... Starting the integration... Starting the integration... Starting the integration... Starting the integration... Computing graph 87/100... Integration finished. Linear algebra computations... Computations finished. Integration finished. Linear algebra computations... The critical eigenvalue is not in the range of the dispersion relation. The linear analysis cannot be performed. The critical eigenvalue is: -2.5393647463732294
/tmp/ipykernel_55793/633668650.py:148: RuntimeWarning: invalid value encountered in scalar divide ipr_eigenvector = np.sum(critical_eigenvector**4) / (np.sum(critical_eigenvector**2)**2)
Computations finished. Integration finished. Linear algebra computations... Computations finished. Integration finished. Linear algebra computations... Computations finished. Integration finished. Linear algebra computations... The critical eigenvalue is not in the range of the dispersion relation. The linear analysis cannot be performed. The critical eigenvalue is: -2.545918372139427
/tmp/ipykernel_55793/633668650.py:148: RuntimeWarning: invalid value encountered in scalar divide ipr_eigenvector = np.sum(critical_eigenvector**4) / (np.sum(critical_eigenvector**2)**2)
Computations finished. Integration finished. Linear algebra computations... Computations finished. Integration finished. Linear algebra computations... The critical eigenvalue is not in the range of the dispersion relation. The linear analysis cannot be performed. The critical eigenvalue is: -2.1652201325005853
/tmp/ipykernel_55793/633668650.py:148: RuntimeWarning: invalid value encountered in scalar divide ipr_eigenvector = np.sum(critical_eigenvector**4) / (np.sum(critical_eigenvector**2)**2)
Computations finished. Integration finished. Linear algebra computations... Computations finished. Starting the integration...Starting the integration...Starting the integration...Starting the integration... Starting the integration... Starting the integration...Starting the integration... Starting the integration... Computing graph 88/100... Integration finished. Linear algebra computations... The critical eigenvalue is not in the range of the dispersion relation. The linear analysis cannot be performed. The critical eigenvalue is: -2.2591066991801916 Computations finished. Integration finished. Linear algebra computations... The critical eigenvalue is not in the range of the dispersion relation. The linear analysis cannot be performed. The critical eigenvalue is: -2.3676975114945655
/tmp/ipykernel_55793/633668650.py:148: RuntimeWarning: invalid value encountered in scalar divide ipr_eigenvector = np.sum(critical_eigenvector**4) / (np.sum(critical_eigenvector**2)**2)
Computations finished. Integration finished. Linear algebra computations... Computations finished. Integration finished. Linear algebra computations... The critical eigenvalue is not in the range of the dispersion relation. The linear analysis cannot be performed. The critical eigenvalue is: 8.881784197001252e-16
/tmp/ipykernel_55793/633668650.py:148: RuntimeWarning: invalid value encountered in scalar divide ipr_eigenvector = np.sum(critical_eigenvector**4) / (np.sum(critical_eigenvector**2)**2)
Computations finished. Integration finished. Linear algebra computations... Computations finished. Integration finished. Linear algebra computations... Integration finished. Computations finished.Linear algebra computations... The critical eigenvalue is not in the range of the dispersion relation. The linear analysis cannot be performed. The critical eigenvalue is: -2.4768759452845495
/tmp/ipykernel_55793/633668650.py:148: RuntimeWarning: invalid value encountered in scalar divide ipr_eigenvector = np.sum(critical_eigenvector**4) / (np.sum(critical_eigenvector**2)**2)
Computations finished. Integration finished. Linear algebra computations... The critical eigenvalue is not in the range of the dispersion relation. The linear analysis cannot be performed. The critical eigenvalue is: -2.457538677667931
/tmp/ipykernel_55793/633668650.py:148: RuntimeWarning: invalid value encountered in scalar divide ipr_eigenvector = np.sum(critical_eigenvector**4) / (np.sum(critical_eigenvector**2)**2)
Computations finished. Starting the integration...Starting the integration...Starting the integration...Starting the integration... Starting the integration... Starting the integration...Starting the integration...Starting the integration... Computing graph 89/100... Integration finished. Linear algebra computations... The critical eigenvalue is not in the range of the dispersion relation. The linear analysis cannot be performed. The critical eigenvalue is: -2.529875503227853 Computations finished. Integration finished. Linear algebra computations... The critical eigenvalue is not in the range of the dispersion relation. The linear analysis cannot be performed. The critical eigenvalue is: -2.4395505121558343
/tmp/ipykernel_55793/633668650.py:148: RuntimeWarning: invalid value encountered in scalar divide ipr_eigenvector = np.sum(critical_eigenvector**4) / (np.sum(critical_eigenvector**2)**2)
Computations finished. Integration finished. Linear algebra computations... The critical eigenvalue is not in the range of the dispersion relation. The linear analysis cannot be performed. The critical eigenvalue is: -2.3157374346599044 Computations finished. Integration finished. Linear algebra computations... The critical eigenvalue is not in the range of the dispersion relation. The linear analysis cannot be performed. The critical eigenvalue is: -2.6929750101459025 Computations finished. Integration finished. Linear algebra computations... Integration finished.Computations finished. Linear algebra computations... The critical eigenvalue is not in the range of the dispersion relation. The linear analysis cannot be performed. The critical eigenvalue is: -8.881784197001252e-16 Computations finished. Integration finished. Linear algebra computations... The critical eigenvalue is not in the range of the dispersion relation. The linear analysis cannot be performed. The critical eigenvalue is: -1.3560011292923596e-15 Computations finished. Integration finished. Linear algebra computations... Computations finished. Starting the integration...Starting the integration...Starting the integration...Starting the integration...Starting the integration...Starting the integration... Starting the integration...Starting the integration... Computing graph 90/100... Integration finished. Linear algebra computations... The critical eigenvalue is not in the range of the dispersion relation. Integration finished. The linear analysis cannot be performed.Linear algebra computations... The critical eigenvalue is: 1.3322676295501878e-15 Computations finished. The critical eigenvalue is not in the range of the dispersion relation. The linear analysis cannot be performed. The critical eigenvalue is: -1.7763568394002505e-15 Computations finished. Integration finished. Linear algebra computations... The critical eigenvalue is not in the range of the dispersion relation. The linear analysis cannot be performed. The critical eigenvalue is: -2.7631972248629397 Computations finished. Integration finished. Linear algebra computations... Computations finished. Integration finished. Linear algebra computations... The critical eigenvalue is not in the range of the dispersion relation. The linear analysis cannot be performed. The critical eigenvalue is: -2.8117702911145477 Computations finished. Integration finished. Linear algebra computations... Computations finished. Integration finished. Linear algebra computations... The critical eigenvalue is not in the range of the dispersion relation. The linear analysis cannot be performed. The critical eigenvalue is: 5.917350894406997e-16
/tmp/ipykernel_55793/633668650.py:148: RuntimeWarning: invalid value encountered in scalar divide ipr_eigenvector = np.sum(critical_eigenvector**4) / (np.sum(critical_eigenvector**2)**2)
Computations finished. Integration finished. Linear algebra computations... The critical eigenvalue is not in the range of the dispersion relation. The linear analysis cannot be performed. The critical eigenvalue is: -1.7763568394002505e-15
/tmp/ipykernel_55793/633668650.py:148: RuntimeWarning: invalid value encountered in scalar divide ipr_eigenvector = np.sum(critical_eigenvector**4) / (np.sum(critical_eigenvector**2)**2)
Computations finished. Starting the integration...Starting the integration...Starting the integration...Starting the integration...Starting the integration...Starting the integration... Starting the integration...Starting the integration... Computing graph 91/100... Integration finished. Linear algebra computations... The critical eigenvalue is not in the range of the dispersion relation. The linear analysis cannot be performed. The critical eigenvalue is: -1.7763568394002505e-15 Computations finished. Integration finished. Linear algebra computations... The critical eigenvalue is not in the range of the dispersion relation. The linear analysis cannot be performed. The critical eigenvalue is: -4.440892098500626e-16 Computations finished. Integration finished. Linear algebra computations... The critical eigenvalue is not in the range of the dispersion relation. The linear analysis cannot be performed. The critical eigenvalue is: 4.440892098500626e-16 Computations finished. Integration finished. Linear algebra computations... The critical eigenvalue is not in the range of the dispersion relation. The linear analysis cannot be performed. The critical eigenvalue is: 0.0 Computations finished. Integration finished. Linear algebra computations... The critical eigenvalue is not in the range of the dispersion relation. The linear analysis cannot be performed. The critical eigenvalue is: 4.440892098500626e-16
/tmp/ipykernel_55793/633668650.py:148: RuntimeWarning: invalid value encountered in scalar divide ipr_eigenvector = np.sum(critical_eigenvector**4) / (np.sum(critical_eigenvector**2)**2)
Computations finished. Integration finished. Linear algebra computations... The critical eigenvalue is not in the range of the dispersion relation. The linear analysis cannot be performed. The critical eigenvalue is: 0.0 Computations finished. Integration finished. Linear algebra computations... The critical eigenvalue is not in the range of the dispersion relation. The linear analysis cannot be performed. The critical eigenvalue is: -2.184989577114578 Computations finished. Integration finished. Linear algebra computations... The critical eigenvalue is not in the range of the dispersion relation. The linear analysis cannot be performed. The critical eigenvalue is: -2.4982417285529586 Computations finished. Starting the integration... Starting the integration...Starting the integration...Starting the integration...Starting the integration...Starting the integration... Starting the integration... Starting the integration... Computing graph 92/100... Integration finished. Linear algebra computations... The critical eigenvalue is not in the range of the dispersion relation. The linear analysis cannot be performed. The critical eigenvalue is: 8.881784197001252e-16 Computations finished. Integration finished. Linear algebra computations... The critical eigenvalue is not in the range of the dispersion relation. The linear analysis cannot be performed. The critical eigenvalue is: 8.881784197001252e-16 Computations finished. Integration finished. Linear algebra computations... The critical eigenvalue is not in the range of the dispersion relation. Integration finished. The linear analysis cannot be performed.Linear algebra computations... The critical eigenvalue is: 0.0 The critical eigenvalue is not in the range of the dispersion relation.Computations finished. The linear analysis cannot be performed. The critical eigenvalue is: 1.3322676295501878e-15 Computations finished. Integration finished. Linear algebra computations... The critical eigenvalue is not in the range of the dispersion relation. The linear analysis cannot be performed. The critical eigenvalue is: -5.656712314709048e-15 Computations finished. Integration finished. Linear algebra computations... The critical eigenvalue is not in the range of the dispersion relation. The linear analysis cannot be performed. The critical eigenvalue is: 0.0 Computations finished. Integration finished. Linear algebra computations... The critical eigenvalue is not in the range of the dispersion relation. The linear analysis cannot be performed. The critical eigenvalue is: -5.0180997951793105e-15 Computations finished. Integration finished. Linear algebra computations... The critical eigenvalue is not in the range of the dispersion relation. The linear analysis cannot be performed. The critical eigenvalue is: -1.377710667796089e-15 Computations finished. Starting the integration...Starting the integration...Starting the integration...Starting the integration...Starting the integration...Starting the integration...Starting the integration...Starting the integration... Computing graph 93/100... Integration finished. Linear algebra computations... The critical eigenvalue is not in the range of the dispersion relation. The linear analysis cannot be performed. The critical eigenvalue is: -8.881784197001252e-16 Computations finished. Integration finished. Linear algebra computations... The critical eigenvalue is not in the range of the dispersion relation. The linear analysis cannot be performed. The critical eigenvalue is: 4.234351599827366e-16 Computations finished. Integration finished. Linear algebra computations... The critical eigenvalue is not in the range of the dispersion relation. The linear analysis cannot be performed. The critical eigenvalue is: -5.2889700095621834e-15 Computations finished. Integration finished. Linear algebra computations... The critical eigenvalue is not in the range of the dispersion relation. The linear analysis cannot be performed. The critical eigenvalue is: 1.9051493342871517e-15 Computations finished. Integration finished. Linear algebra computations... Integration finished. Linear algebra computations...The critical eigenvalue is not in the range of the dispersion relation. The linear analysis cannot be performed. The critical eigenvalue is not in the range of the dispersion relation.The critical eigenvalue is: The linear analysis cannot be performed.-4.440892098500626e-16 The critical eigenvalue is: Computations finished. -8.881784197001252e-16 Computations finished. Integration finished. Integration finished.Linear algebra computations... Linear algebra computations... The critical eigenvalue is not in the range of the dispersion relation. The critical eigenvalue is not in the range of the dispersion relation.The linear analysis cannot be performed. The linear analysis cannot be performed.The critical eigenvalue is: The critical eigenvalue is: 0.0 8.881784197001252e-16Computations finished. Computations finished. Starting the integration...Starting the integration...Starting the integration...Starting the integration...Starting the integration...Starting the integration... Starting the integration... Starting the integration... Computing graph 94/100... Integration finished. Linear algebra computations... The critical eigenvalue is not in the range of the dispersion relation. The linear analysis cannot be performed. The critical eigenvalue is: -8.881784197001252e-16 Computations finished. Integration finished. Linear algebra computations... The critical eigenvalue is not in the range of the dispersion relation. The linear analysis cannot be performed. The critical eigenvalue is: 0.0 Computations finished. Integration finished. Linear algebra computations... The critical eigenvalue is not in the range of the dispersion relation. The linear analysis cannot be performed. The critical eigenvalue is: 3.3164948617519065e-15 Computations finished. Integration finished. Linear algebra computations... The critical eigenvalue is not in the range of the dispersion relation. The linear analysis cannot be performed. The critical eigenvalue is: -1.1539287319758375e-15 Computations finished. Integration finished. Linear algebra computations... The critical eigenvalue is not in the range of the dispersion relation. The linear analysis cannot be performed. The critical eigenvalue is: -8.881784197001252e-16 Computations finished. Integration finished. Linear algebra computations... The critical eigenvalue is not in the range of the dispersion relation. The linear analysis cannot be performed. The critical eigenvalue is: -1.7763568394002505e-15 Computations finished. Integration finished. Linear algebra computations... The critical eigenvalue is not in the range of the dispersion relation. The linear analysis cannot be performed. The critical eigenvalue is: -8.881784197001252e-16 Computations finished. Integration finished. Linear algebra computations... The critical eigenvalue is not in the range of the dispersion relation. The linear analysis cannot be performed. The critical eigenvalue is: 1.0007570361716873e-15 Computations finished. Starting the integration...Starting the integration... Starting the integration...Starting the integration...Starting the integration...Starting the integration...Starting the integration...Starting the integration... Computing graph 95/100... Integration finished. Linear algebra computations... The critical eigenvalue is not in the range of the dispersion relation. The linear analysis cannot be performed. The critical eigenvalue is: 8.881784197001252e-16 Computations finished. Integration finished. Linear algebra computations... The critical eigenvalue is not in the range of the dispersion relation. The linear analysis cannot be performed. The critical eigenvalue is: 8.881784197001252e-16 Computations finished. Integration finished. Linear algebra computations... The critical eigenvalue is not in the range of the dispersion relation. The linear analysis cannot be performed. The critical eigenvalue is: 1.7763568394002505e-15 Computations finished. Integration finished. Linear algebra computations... The critical eigenvalue is not in the range of the dispersion relation. The linear analysis cannot be performed. The critical eigenvalue is: -8.881784197001252e-16 Computations finished. Integration finished. Linear algebra computations... The critical eigenvalue is not in the range of the dispersion relation. The linear analysis cannot be performed. The critical eigenvalue is: -2.6645352591003757e-15 Computations finished. Integration finished. Linear algebra computations... Integration finished. The critical eigenvalue is not in the range of the dispersion relation.Linear algebra computations... The linear analysis cannot be performed. The critical eigenvalue is: The critical eigenvalue is not in the range of the dispersion relation. 1.7763568394002505e-15The linear analysis cannot be performed. Computations finished.The critical eigenvalue is: -2.6645352591003757e-15 Computations finished. Integration finished. Linear algebra computations... The critical eigenvalue is not in the range of the dispersion relation. The linear analysis cannot be performed. The critical eigenvalue is: -1.963710006122749e-15 Computations finished. Starting the integration...Starting the integration...Starting the integration...Starting the integration...Starting the integration...Starting the integration...Starting the integration... Starting the integration... Computing graph 96/100... Integration finished. Linear algebra computations... The critical eigenvalue is not in the range of the dispersion relation. The linear analysis cannot be performed. The critical eigenvalue is: -1.7763568394002505e-15 Computations finished. Integration finished. Linear algebra computations... The critical eigenvalue is not in the range of the dispersion relation. The linear analysis cannot be performed. The critical eigenvalue is: -2.129302624024876e-15 Computations finished. Integration finished. Linear algebra computations... Integration finished. The critical eigenvalue is not in the range of the dispersion relation.Linear algebra computations... The linear analysis cannot be performed. The critical eigenvalue is: The critical eigenvalue is not in the range of the dispersion relation.-1.7763568394002505e-15 The linear analysis cannot be performed. Computations finished.The critical eigenvalue is: 3.3981721674106285e-15 Computations finished. Integration finished. Linear algebra computations... The critical eigenvalue is not in the range of the dispersion relation. The linear analysis cannot be performed. The critical eigenvalue is: 3.0341378075920944e-15 Computations finished. Integration finished. Linear algebra computations... The critical eigenvalue is not in the range of the dispersion relation. The linear analysis cannot be performed. The critical eigenvalue is: -2.285693916740988e-15 Computations finished. Integration finished. Linear algebra computations... The critical eigenvalue is not in the range of the dispersion relation. The linear analysis cannot be performed. The critical eigenvalue is: -1.1101265337434621e-15 Computations finished. Integration finished. Linear algebra computations... The critical eigenvalue is not in the range of the dispersion relation. The linear analysis cannot be performed. The critical eigenvalue is: 4.403836223964361e-15 Computations finished. Starting the integration...Starting the integration...Starting the integration...Starting the integration...Starting the integration... Starting the integration... Starting the integration... Starting the integration... Computing graph 97/100... Integration finished. Linear algebra computations... The critical eigenvalue is not in the range of the dispersion relation. The linear analysis cannot be performed. The critical eigenvalue is: -4.970809807355093e-16 Computations finished. Integration finished. Linear algebra computations... The critical eigenvalue is not in the range of the dispersion relation. The linear analysis cannot be performed. The critical eigenvalue is: -8.881784197001252e-16 Computations finished. Integration finished. Linear algebra computations... The critical eigenvalue is not in the range of the dispersion relation. The linear analysis cannot be performed. The critical eigenvalue is: 1.0540052542774768e-15 Computations finished. Integration finished. Linear algebra computations... The critical eigenvalue is not in the range of the dispersion relation. The linear analysis cannot be performed. The critical eigenvalue is: 0.0 Computations finished. Integration finished. Linear algebra computations... The critical eigenvalue is not in the range of the dispersion relation. The linear analysis cannot be performed. The critical eigenvalue is: 8.881784197001252e-16 Computations finished. Integration finished. Linear algebra computations... The critical eigenvalue is not in the range of the dispersion relation. The linear analysis cannot be performed. The critical eigenvalue is: 1.509429278524096e-15 Computations finished. Integration finished.Integration finished. Linear algebra computations...Linear algebra computations... The critical eigenvalue is not in the range of the dispersion relation.The critical eigenvalue is not in the range of the dispersion relation. The linear analysis cannot be performed.The linear analysis cannot be performed. The critical eigenvalue is: The critical eigenvalue is: -6.565892017633031e-16-5.40972761303715e-15 Computations finished. Computations finished. Starting the integration...Starting the integration... Starting the integration...Starting the integration...Starting the integration...Starting the integration... Starting the integration... Computing graph 98/100... Starting the integration... Integration finished. Linear algebra computations... The critical eigenvalue is not in the range of the dispersion relation. The linear analysis cannot be performed. The critical eigenvalue is: -8.881784197001252e-16 Computations finished. Integration finished. Linear algebra computations... The critical eigenvalue is not in the range of the dispersion relation. The linear analysis cannot be performed. The critical eigenvalue is: 2.4496634653628537e-15 Computations finished. Integration finished. Linear algebra computations... Integration finished.The critical eigenvalue is not in the range of the dispersion relation. Linear algebra computations... The linear analysis cannot be performed. The critical eigenvalue is: The critical eigenvalue is not in the range of the dispersion relation.0.0 The linear analysis cannot be performed.Computations finished. The critical eigenvalue is: 1.0067009351638022e-15 Computations finished. Integration finished. Linear algebra computations... The critical eigenvalue is not in the range of the dispersion relation. The linear analysis cannot be performed. The critical eigenvalue is: 8.881784197001252e-16 Computations finished. Integration finished. Linear algebra computations... The critical eigenvalue is not in the range of the dispersion relation. The linear analysis cannot be performed. Integration finished.The critical eigenvalue is: Linear algebra computations...-3.364222517974507e-15 Computations finished. The critical eigenvalue is not in the range of the dispersion relation. The linear analysis cannot be performed. The critical eigenvalue is: -2.8199062527937e-15 Computations finished. Integration finished. Linear algebra computations... The critical eigenvalue is not in the range of the dispersion relation. The linear analysis cannot be performed. The critical eigenvalue is: 1.2079864686876847e-15 Computations finished. Starting the integration...Starting the integration...Starting the integration...Starting the integration...Starting the integration...Starting the integration... Starting the integration... Starting the integration... Computing graph 99/100... Integration finished. Linear algebra computations... The critical eigenvalue is not in the range of the dispersion relation. The linear analysis cannot be performed. The critical eigenvalue is: 3.552713678800501e-15 Computations finished. Integration finished. Linear algebra computations... The critical eigenvalue is not in the range of the dispersion relation. The linear analysis cannot be performed.Integration finished. The critical eigenvalue is: Linear algebra computations...1.7763568394002505e-15 Computations finished. The critical eigenvalue is not in the range of the dispersion relation. The linear analysis cannot be performed. The critical eigenvalue is: 1.0113397725625435e-16 Computations finished. Integration finished. Linear algebra computations... The critical eigenvalue is not in the range of the dispersion relation. The linear analysis cannot be performed. The critical eigenvalue is: -2.1476787684794742e-15 Computations finished. Integration finished. Linear algebra computations... The critical eigenvalue is not in the range of the dispersion relation.Integration finished. The linear analysis cannot be performed.Linear algebra computations... The critical eigenvalue is: -4.178887069980057e-15 The critical eigenvalue is not in the range of the dispersion relation. Computations finished.The linear analysis cannot be performed. The critical eigenvalue is: -1.0561632216261665e-15Integration finished. Computations finished.Linear algebra computations... The critical eigenvalue is not in the range of the dispersion relation. The linear analysis cannot be performed. The critical eigenvalue is: 4.176751134223985e-16 Computations finished. Integration finished. Linear algebra computations... The critical eigenvalue is not in the range of the dispersion relation. The linear analysis cannot be performed. The critical eigenvalue is: -9.374678378614101e-16 Computations finished. Starting the integration...Starting the integration...Starting the integration... Starting the integration... Starting the integration...Starting the integration...Starting the integration...Starting the integration... Computing graph 100/100... Integration finished.Integration finished. Linear algebra computations... Linear algebra computations... The critical eigenvalue is not in the range of the dispersion relation.The critical eigenvalue is not in the range of the dispersion relation. The linear analysis cannot be performed. The linear analysis cannot be performed.The critical eigenvalue is: Integration finished. Linear algebra computations...The critical eigenvalue is: 3.552713678800501e-15 -4.17364950999942e-15 Computations finished.The critical eigenvalue is not in the range of the dispersion relation. Computations finished. The linear analysis cannot be performed. The critical eigenvalue is: -2.273002726061519e-16 Computations finished. Integration finished. Linear algebra computations... The critical eigenvalue is not in the range of the dispersion relation. The linear analysis cannot be performed. The critical eigenvalue is: -8.881784197001252e-16 Integration finished.Computations finished. Linear algebra computations... The critical eigenvalue is not in the range of the dispersion relation. The linear analysis cannot be performed. The critical eigenvalue is: 5.329070518200751e-15 Computations finished. Integration finished.Integration finished. Linear algebra computations...Linear algebra computations... The critical eigenvalue is not in the range of the dispersion relation.The critical eigenvalue is not in the range of the dispersion relation. The linear analysis cannot be performed.The linear analysis cannot be performed. The critical eigenvalue is: The critical eigenvalue is: 4.516563007987751e-15-3.3988684354622447e-16 Computations finished.Computations finished. Integration finished. Linear algebra computations... The critical eigenvalue is not in the range of the dispersion relation. The linear analysis cannot be performed. The critical eigenvalue is: -9.70043214339077e-16 Computations finished. Plotting the results...
{'dynamics_data': {np.float64(0.0001): [{'critical_eigenvalue': -1.2603186817795815, 'last_values_rho': [0.007913275673366504, 0.0079137213698872, 0.00792086863887327, 0.007924633443712513, 0.007927862752940728, 0.007932827348254883, 0.007938302369854327, 0.00794229008751715, 0.007945491981655678, 0.007948526881856427, 0.007949197868726953, 0.007948800901346063, 0.007949489665583776, 0.007950013804775908, 0.007944957387392268, 0.007942828303165117, 0.007892622434129571, 0.00775142662833852, 0.007537730023815444, 0.008237539975774312, 0.00793977740265393, 0.00794000730297712, 0.007935757027423385, 0.007943123227857556, 0.007940643476611388, 0.007938197841319366, 0.00793754648010574, 0.007942902660335854, 0.007938944271039451, 0.007940397393264324, 0.007943632170682089, 0.007939758658543484, 0.0079414870322974, 0.00793882931621006, 0.007938710277047591, 0.007934940509819962, 0.007933925871180983, 0.007939842590447492, 0.00794265257199038, 0.007942564812461167, 0.007940253310958214, 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14.666666666666666, 14.566666666666666, 14.566666666666666], [15.2, 15.166666666666666, 15.1, 15.366666666666667, 15.333333333333334, 15.266666666666667, 15.166666666666666, 15.233333333333333], [16.0, 16.0, 16.0, 16.0, 16.0, 16.0, 16.0, 16.0]]}
Antes del cambio de fase¶
In [25]:
# Generate a small world graph with p=0.3
# graph = nx.newman_watts_strogatz_graph(n=60, k=8, p=0.39, seed=40)
graph = nx.newman_watts_strogatz_graph(n=60, k=8, p=0.01, seed=40)
# Draw the graph with a circular layout
plt.figure(figsize=(10, 10))
pos = nx.circular_layout(graph)
nx.draw(graph, pos, node_size=50, node_color='blue', with_labels=False)
plt.title("Small World Graph with p=0.01 (Circular Layout)")
plt.show()
In [ ]:
# # Create an empty graph
# G = nx.Graph()
# # Add nodes
# nodes = range(1, 17)
# G.add_nodes_from(nodes)
# # Add edges based on the visual structure
# edges = [
# (1, 2), (1, 3), (1, 4), (2, 4), (2,5), (3, 4), (3, 6), (3, 7), (3, 8), (4, 5), (4, 8), (4, 9),
# (5, 9), (6, 7), (7, 8), (7, 11), (7, 10), (7, 13), (8, 9), (8, 11), (8, 12), (9, 12),
# (10, 13), (11, 12), (11, 13), (11, 14), (12, 14), (12, 15), (13, 14), (13, 16) ,(14, 15),
# (14, 16), (15, 16)
# ]
# G.add_edges_from(edges)
# graph = G
In [15]:
dyn_1 = get_dynamics(graph, params, plot=True)
Starting the integration... Integration finished. Linear algebra computations...
Computations finished.
Justo en el cambio de fase¶
In [ ]:
# Generate a small world graph with p=0.3
# graph = nx.newman_watts_strogatz_graph(n=60, k=8, p=0.39, seed=40)
graph = nx.newman_watts_strogatz_graph(n=60, k=8, p=0.39, seed=40)
# Draw the graph with a circular layout
plt.figure(figsize=(10, 10))
pos = nx.circular_layout(graph)
nx.draw(graph, pos, node_size=50, node_color='blue', with_labels=False)
plt.title("Small World Graph with p=0.3 (Circular Layout)")
plt.show()
In [21]:
dyn_1 = get_dynamics(graph, params, plot=True)
Starting the integration... Integration finished. Linear algebra computations... The critical eigenvalue is not in the range of the dispersion relation. The linear analysis cannot be performed. The critical eigenvalue is: 2.220446049250313e-15
Computations finished.
/tmp/ipykernel_55793/633668650.py:148: RuntimeWarning: invalid value encountered in scalar divide ipr_eigenvector = np.sum(critical_eigenvector**4) / (np.sum(critical_eigenvector**2)**2)
Después del cambio de fase¶
In [18]:
# Generate a small world graph with p=0.3
# graph = nx.newman_watts_strogatz_graph(n=60, k=8, p=0.39, seed=40)
graph = nx.newman_watts_strogatz_graph(n=60, k=8, p=0.8, seed=40)
# Draw the graph with a circular layout
plt.figure(figsize=(10, 10))
pos = nx.circular_layout(graph)
nx.draw(graph, pos, node_size=50, node_color='blue', with_labels=False)
plt.title("Small World Graph with p=0.3 (Circular Layout)")
plt.show()
In [19]:
dyn_1 = get_dynamics(graph, params, plot=True)
Starting the integration... Integration finished. Linear algebra computations... The critical eigenvalue is not in the range of the dispersion relation. The linear analysis cannot be performed. The critical eigenvalue is: -2.6645352591003757e-15
Computations finished.
/tmp/ipykernel_55793/633668650.py:148: RuntimeWarning: invalid value encountered in scalar divide ipr_eigenvector = np.sum(critical_eigenvector**4) / (np.sum(critical_eigenvector**2)**2)